Welcome to **AMBiPi (**Read as**: एम्बीपाई) (Amans Maths Blogs)**. JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get * JEE Main Math Previous Year Paper Properties and Solutions of Triangles Questions Answer Keys Solutions*.

### JEE Mains Mathematics Properties and Solutions of Triangles Questions Bank

**JEE Properties and Solutions of Triangles Questions No:1**

The sides of a triangle are 3x + 4y, 4x + 3y and 5x + 5y where x, y > 0 then the triangle is

**[2002]**

**Option A**: Right angled

**Option B**: Obtuse angled

**Option C**: Equilateral

**Option D**: None of these

**Show/Hide Answer Key**

**Option B: Obtuse angled**

**JEE Main Properties and Solutions of Triangles Questions No:2**

In a triangle with sides a, b, c, r_{1} > r_{2}> r_{3} (which are the ex-radii) then

**[2002]**

**Option A**: a > b > c

**Option B**: a < b < c

**Option C**: a > b and b < c

**Option D**: a < b and b > c

**Show/Hide Answer Key**

**Option C: a > b > c**

**JEE Mathematics Properties and Solutions of Triangles Questions No: 3**

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

**[2003]**

**Option A**: n(a/4) cot (π/2n)

**Option B**: a cot (π/n)

**Option C**: (a/2) cot (π/2n)

**Option D**: a cot (π/2n)

**Show/Hide Answer Key**

**Option B: A (a/2) cot (π/2n)**

**JEE Main Math Properties and Solutions of Triangles Questions No: 4**

In a triangle ABC, medians AD and BE are drawn. If AD = 4, ∠DAB = 6 and ∠ABE= (π/3) , then the area of the ∆ABC is

**[2003]**

**Option A**: 64/3

**Option B**: 8/3

**Option C**: 16/3

**Option D**: 32/3√ 3

**Show/Hide Answer Key**

**Option D: 32/3√3**

**Properties and Solutions of Triangles JEE Questions No: 5**

If in a ∆ABC a cos^{2} (C/2) + cos^{2} (A/2) = 3b/2 then the sides a, b and c

**[2003]**

**Option A**: Satisfy a + b =c

**Option B**: Are in A.P

**Option C**: Are in G.P

**Option D**: Are in H.P

**Show/Hide Answer Key**

**Option B: Are in A.P**

**Properties and Solutions of Triangles JEE Main Questions No: 6**

The sides of a triangle are sin α, cos α and √1 + sin α cos α for some 0 < α < (π/2). Then the greatest angle of the triangle is

**[2004]**

**Option A**: 150^{o}

**Option B**: 90^{o}

**Option C**: 120^{o}

**Option D**: 60^{o}

**Show/Hide Answer Key**

**Option C: 120 ^{o}**

**Properties and Solutions of Triangles Questions for JEE Mains Questions No: 7 **

In a triangle ∆ABC, let ∠C = (π/2). If r is the inradius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

**[2005]**

**Option A**: b+ c

**Option B**: a + b

**Option C**: a + b + c

**Option D**: c + a

**Show/Hide Answer Key**

**Option B: a + b**

**Properties and Solutions of Triangles Questions and Answers No: 8**

If in a ∆ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in

**[2005]**

**Option A**: G.P

**Option B**: A.P

**Option C**: A.P – G.P

**Option D**: H.P

**Show/Hide Answer Key**

**Option B: A.P**

**Properties and Solutions of Triangles Questions with Solutions No:9**

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

**[2010]**

**Option A**: There is a regular polygon with (r/R) = (1/√2)

**Option B**: There is a regular polygon with (r/R) = (3/2)

**Option C**: There is a regular polygon with (r/R) = (√3/2)

**Option D**: There is a regular polygon with (r/R) = (1/2)

**Show/Hide Answer Key**

**Option B: There is a regular polygon with (r/R) = (3/2)**

**JEE Mains Properties and Solutions of Triangles Questions No: 10**

In a ∆PQR, If 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to

**[2012]**

**Option A**: π/6

**Option B**: π/6

**Option C**: π/4

**Option D**: 3π/4

**Show/Hide Answer Key**

**Option B: π/6**

**JEE Mains Math Properties and Solutions of Triangles Questions No: 11**

ABCD is a trapezium such that AB and CD are parallel and BC ⟂ CD. If ∠ADB = 0, BC = p and CD = q, then AB is equal to

**[2013]**

**Option A**: ( (p^{2 }+ q^{2} ) sinθ / p cosθ + q sinθ)

**Option B**: ( (p^{2 }+ q^{2} ) cosθ / p cosθ + q sinθ)

**Option C**: ( (p^{2 }+ q^{2} ) / p^{2} cosθ + q^{2} sinθ)

**Option D**: ( (p^{2 }+ q^{2} ) sinθ / p cosθ + q sinθ)^{2}

**Show/Hide Answer Key**

**Option A: ( (p ^{2 }+ q^{2}) sinθ / p cos + q sinθ)**

**Properties and Solutions of Triangles Questions for JEE Questions No:12**

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter is

**[2018]**

**Option A**: 3√5/2

**Option B**: √10

**Option C**: ω^{2}_{0}= 1/LC

**Option D**: 3 √5/√2

**Show/Hide Answer Key**

**Option D: 3** √5 / √2

**Properties and Solutions of Triangles Problems for Class 11 Questions No: 13**

In a ∆ABC = (a/b) = 2 + √3 and ∠C = 60°. Then the ordered pair (∠A, ∠B) is equal to

**[2019]**

**Option A**: (45°,75°)

**Option B**: (105°, 15°)

**Option C**: (15°, 105°)

**Option D**: (75°, 45°)

**Show/Hide Answer Key**

**Option B: (105°, 15°)**

**Properties and Solutions of Triangles Problems for Class 12 Questions No: 14**

With the usual notation, in ∆ABC, if ∠A + ∠B = 120°, a = √3 + 1 and b = √3 – 1, then the ratio ∠A : ∠B, is:

**[2019]**

**Option A**: 7 : 1

**Option B**: 5 : 3

**Option C**: 9 : 7

**Option D**: 3 : 1

**Show/Hide Answer Key**

**Option A: 7 : 1**

**Properties and Solutions of Triangles Problems for Class 11 JEE Questions No: 15**

Given (b + c / 11) = (c + a / 12) = (a + b / 13) for a ∆ABC with usual notation. If (cosA /α) = (cosB / β) = (cosC / γ) then the ordered traid (α, β, γ) has a value

**[2019]**

**Option A**: (7,19,25)

**Option B**: (3,4,5)

**Option C**: (5, 12, 13)

**Option D**: (19,7,25)

**Show/Hide Answer Key**

**Option A: (7,19,25)**

**Properties and Solutions of Triangles Problems for Class 12 JEE Questions No: 16**

In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y. If x^{2 }– c^{2 }= y, where c is the length of the third side of the triangle, then the circumradius of the triangle is

**[2019]**

**Option A**: 3/2y

**Option B**: c/√3

**Option C**: c/3

**Option D**: y/√3

**Show/Hide Answer Key**

**Option B: c/√3**

**JEE Properties and Solutions of Triangles Questions No:17**

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is

**[2019]**

**Option A**: 5 : 9 : 13

**Option B**: 4 : 5 : 6

**Option C**: 3 : 4 : 5

**Option D**: 5 : 6 : 7

**Show/Hide Answer Key**

**Option B: 4 : 5 : 6**

**JEE Main Properties and Solutions of Triangles Questions No:18**

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : √3. If c = 4 cm, then the area (in sq.cm) of this triangle is:

**[2019]**

**Option A**: 2/√3

**Option B**: 4√3

**Option C**: 2√3

**Option D**: 4√3

**Show/Hide Answer Key**

**Option C: 2√3**

**JEE Mathematics Properties and Solutions of Triangles Questions No: 19**

Let A (3, 0, -1), B (2, 10, 6) and C (1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2:1, then cos (O being the origin) is equal to

**[2019]**

**Option A**: 1/2√15

**Option B**: 1/√15

**Option C**: 1/6√10

**Option D**: 1/√30

**Show/Hide Answer Key**

**Option B: 1/ √15**

**JEE Main Math Properties and Solutions of Triangles Questions No: 20**

The area bounded by the lines y = | |x – 1| – 2| is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : Bonus**

**Properties and Solutions of Triangles JEE Questions No: 21**

In ∆ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of ∆ABC is 30 cm^{2} and R and r are respectively the radii of circumcircle and incircle of ∆ABC, then the value of 2R + r (in cm) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 15**

**Properties and Solutions of Triangles JEE Main Questions No: 22**

Let A(-1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0, intersects lines AC and BC at point P and Q respectively. Let A_{1} and A_{2} be the areas of ∆ABC and ∆PQC respectively, such that A_{1} = 3A_{2}, then the value of m is equal to

**[2021]**

**Option A**: 2

**Option B**: 3

**Option C**: 4/15

**Option D**: 1

**Show/Hide Answer Key**

**Option D: 1**

**Properties and Solutions of Triangles Questions for JEE Mains Questions No: 23 **

A square ABCD has all its vertices on the curve x^{2}y^{2} = 1. The midpoints of its sides also lie on the same curve. Then, the square of area of ABCD is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 80**

**Properties and Solutions of Triangles Questions and Answers No: 24**

Consider a triangle having vertices A(-2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point then the value of real number α is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 9**

**Properties and Solutions of Triangles Questions with Solutions No:25**

If in a triangle ABC, AB = 5 units, and radius of circumcircle of ∆ABC is 5 units, then the area (in sq. units) of ∆ABC is

**[2021]**

**Option A**: 10 + 6√2

**Option B**: 8 + 2√2

**Option C**: 6 + 8√3

**Option D**: 4 + 2√3

**Show/Hide Answer Key**

**Option C: 6 + 8√3**

**JEE Mains Properties and Solutions of Triangles Questions No: 26**

If a rectangle is inscribed in an equilateral triangle of side length as shown in the figure, then the square of the largest area of such a rectangle is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 3**

**JEE Mains Math Properties and Solutions of Triangles Questions No: 27**

Two tangents are drawn from the point P(-1, 1) to the circle x^{2} + y^{2 }– 2x – 6y + 6 = 0. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to

**[2021]**

**Option A**: 2

**Option B**: (3√2 + 2)

**Option C**: 4

**Option D**: (3√2 -1)

**Show/Hide Answer Key**

**Option C: 4**

**Properties and Solutions of Triangles Questions for JEE Questions No:28**

The Let (sin A/ sin B) = (sin (A – C) / sin (C – B) ) where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then

**[2021]**

**Option A**: b^{2 }– a^{2} = a^{2} + c^{2}

**Option B**: b^{2 }, c^{2 }, a^{2 } are in A.P

**Option C**: c^{2 }, a^{2 }, b^{2 } are in A.P

**Option D**: a^{2 }, b^{2 }, c^{2 } are in A.P

**Show/Hide Answer Key**

**Option B: b^{2}, c^{2}, a^{2} are in A.P**

**Properties and Solutions of Triangles Problems for Class 11 Questions No: 29**

If the minimum area of the triangle formed by a tangent to the ellipse (x^{2} / b^{2}) + (y^{2} / 4a^{2}) = 1 and the co-ordinate axis is kab, then k is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 2**

**Properties and Solutions of Triangles Problems for Class 12 Questions No: 30**

The Let B be the centre of the circle x^{2} + y^{2 }– 2x + 4y + 1 = 0. Let the tangents at two points P and Q on the circle intersect at the point A(3, 1). Then 8 (area ∆APQ / area ∆BPQ) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 18**

**Properties and Solutions of Triangles Problems for Class 11 JEE Questions No: 31**

A man starts walking from the point P(-3, 4), touches the x axis at R. and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then 50 ( (PR)^{2} + (RQ)^{2 }) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 18**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |