Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20) |
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Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40) |

Properties of Triangle Q. No. 41 to 60 |

Properties of Triangle Q. No. 61 to 80 |

Properties of Triangle Q. No. 81 to 100 |

**Ques No 1:**

In triangle ABC, if and a = 2, then area of triangle ABC is

**Options:**

A. 1

B. 2

C.

D.

**Solution:**

**Ques No 2:**

In triangle ABC, if a = 4, b = 3, angle A = 60 degree. then c is a root of the equation

**Options:**

A. c^{2} – 3c – 7 = 0

B. c^{2} + 3c + 7 = 0

C. c^{2} – 3c + 7 = 0

D. c^{2} + 3c – 7 = 0

**Solution:**

**Ques No 3:**

In cotA/2 = (b + c)/a, then the triangle ABC is

**Options:**

A. Isosceles Triangle

B. Equilateral Triangle

C. Right Angled Triangle

D. None of These

**Solution:**

**Ques No 4:**

In triangle ABC, sin^{2}A + sin^{2}B + sin^{2}C is

**Options:**

A. 0

B. 1

C. -1

D. 2

**Solution:**

**Ques No 5:**

In c^{2} = a^{2} + b^{2}, 2s = a + b + c, then 4s(s – a)(s – b)(s – c) is

**Options:**

A. s^{4}

B. b^{2}c^{2}

C. c^{2}a^{2}

D. a^{2}b^{2}

**Solution:**

**Ques No 6:**

In an equilateral triangle, the inradius, circumcentre and one of ex-radii are in ratio

A. 2 : 3 : 5

B. 1 : 2 : 3

C. 1 : 3 : 7

D. 3 : 7 : 9

**Solution:**

**Ques No 7:**

In triangle ABC, , then the angle A is

A. 30 degree

B. 60 degree

C. 90 degree

D. 45 degree

**Solution:**

**Ques No 8:**

If in triangle ABC, = a^{2} – (b – c)^{2}, then tan(A/2)

A. 15/4

B. 1/4

C. 1/2

D. 1/5

**Solution:**

**Ques No 9:**

Point D, E are taken on the sides BC of triangle ABC such that BD = DE = EC. If angle BAD = x, angle DAE = y, angle EAC = z, then {sin(x + y)sin(y + z)}/(sin x sin z) is

A. 1

B. 2

C. 3

D. 4

**Solution:**

**Ques No 10:**

In triangle ABC, 3a = b + c, then find cot(B/2)cot(C/2)

A. 1

B.

C. 2

D. None of These

**Solution:**

Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20) |
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Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40) |

Properties of Triangle Q. No. 41 to 60 |

Properties of Triangle Q. No. 61 to 80 |

Properties of Triangle Q. No. 81 to 100 |

**Ques No 11:**

If A + B + C = , n Z, then tan(nA) + tan(nB) + tan(nC) is equal to

A. 1

B. 0

C. tan(nA)tan(nB)tan(nC)

D. None of These

**Solution:**

**Ques No 12:**

If triangle ABC, (b + c)/11 = (c + a) /12 = (a + b)/13, then cos A is

A. 1/5

B. 5/7

C. 19/35

D. None of These

**Solution:**

**Ques No 13:**

If p_{1}, p_{2}, p_{3} are altitude of triangle ABC from the vertices A, B, C and be the area of the triangle, then p_{1}^{-1} + p_{2}^{-1} – p_{3}^{-1 }is

A. (s – a)/

B. (s – b)/

C. (s – c)/

D. s/

**Solution:**

**Ques No 14:**

In triangle ABC, angle A = 75, angle B = 75, then a + c is

A. 0

B. b

C. 2b

D. -b

**Solution:**

**Ques No 15:**

If in triangle ABC, cos A = (sin B)/(2sin C), then triangle ABC is

A. Equilateral

B. Isosceles

C. Right Angled

D. None of These

**Solution:**

**Ques No 16:**

If r, r_{1}, r_{2}, r_{3} are radius of incircle and excircle, then the value of 1/r_{1} + 1/r_{2} + 1/r_{3} is

A. 1

B. 0

C. 1/r

D. None of These

**Solution:**

**Ques No 17:**

If p_{1}, p_{2}, p_{3} are altitude of triangle ABC from the vertices A, B, C to the opposite sides, then p_{1}p_{2}p_{3}^{ }is

A. (a^{2}b^{2}c^{2})/R^{2}

B. (a^{2}b^{2}c^{2})/4R^{2}

C. (4a^{2}b^{2}c^{2})/R^{2}

D. (a^{2}b^{2}c^{2})/8R^{2}

**Solution:**

**Ques No 18:**

If exradii r_{1}, r_{2}, r_{3} of triangle ABC are in HP then its sides are in

A. AP

B. GP

C. HP

D. None of These

**Solution:**

**Ques No 19:**

In a triangle ABC, (1 – r_{1}/r_{2})(1 – r_{1}/r_{3}) = 2, then the triangle is

A. Right Angled

B. Isosceles

C. Equilateral

D. None of These

**Solution:**

**Ques No 20:**

The value of 1/r_{1}^{2} + 1/r_{2}^{2} + 1/r_{3}^{2} + 1/r^{2} is

A. 0

B. (a^{2} + b^{2} + c^{2})/^{2}

C. ^{2}/(a^{2} + b^{2} + c^{2})

D. (a^{2} + b^{2} + c^{2})/

**Solution:**

Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20) |
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Properties of Triangle Questions With Solutions (Q.No. 21 To Q.No 40) |

Properties of Triangle Q. No. 41 to 60 |

Properties of Triangle Q. No. 61 to 80 |

Properties of Triangle Q. No. 81 to 100 |