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:**

If acosA = bcosB in triangle ABC, then the angle C is

**Options:**

A. 45 degree

B. 60 degree

C. 90 degree

D. None Of These

**Solution:**

**Ques No 2:**

In triangle ABC, if a = 2, B = 60 degree and C = 75 degree, then the value of b is

**Options:**

A.

B.

C. 3

D.

**Solution: **

Read : Trigonometric Conditional Identities Important Questions

**Ques No 3:**

If A, A1, A2, A3 are the areas of incircle and excircles of a triangle, then

**Options:**

A.

B.

C.

D.

**Solution:**

**Ques No 4:**

In triangle ABC, acosA + bcosB + ccosC is

**Options:**

A. r + R

B. r – R

C. 2(r + R)

D. 2(r – R)

**Solution:**

**Ques No 5:**

If in a triangle, the ex-radii r_{1}, r_{2}, r_{3} are in the ratio 1 : 2 : 3, then the sides of the ratio is

**Options:**

A. 5 : 8 : 9

B. 1 : 2 : 3

C. 3 : 5 : 7

D. 1 : 5 : 9

**Solution:**

**Ques No 6:**

If in a triangle, the base of the length of a and the ratio of two sides is r (r < 1), then the maximum value of the altitude is

**Options:**

A. ar

B. ar/(1 + r^{2})

C. ar/(1 – r^{2})

D. a/r

**Solution:**

**Ques No 7:**

If in a triangle ABC, , then the value of cosA + cosB + cosC is

**Options:**

A. 1/48

B. 69/48

C. 50/69

D. None of these

**Solution: **

Read : Trigonometric Maximum & Minimum Important Questions

**Ques No 8:**

In a right angled triangle ABC, cos^{2}A + cos^{2}B + cos^{2}C is

**Options:**

A. 0

B. 1

C. -1

D. None of these

**Solution:**

**Ques No 9:**

In a triangle ABC, if b = 2 cm, c = cm and angle A = /6, then find distance between its circumcentre and incentre

**Options:**

A. 2 +

B.

C.

D. 2 –

**Solution:**

**Ques No 10:**

If x, y and z are respectively be the perpendicular from the circumcentre to the sides of triangle ABC, then the value of a/x + b/y + c/z is

**Options:**

A. (abc)/(xyz)

B. (abc)/(2xyz)

C. (abc)/(3xyz)

D. (abc)/(4xyz)

**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:**

In a triangle ABC, a = 5, b = 4, C = 3, G is the centroid of triangle, then the value of circumradius of triangle GAB is

**Options:**

A. /12

B. 3/12

C. 5/12

D. 7/12

**Solution:**

**Ques No 12:**

If are the distance of the vertices of a triangle from the corresponding point of contact with the incircle, then the value of is

**Options:**

A. r

B. r^{2}

C. 1/r

D. 1/r^{2}

**Solution:**

**Ques No 13:**

If the median AD of a triangle ABC is perpendicular to AB, then the value of tanA + 2tanB is

**Options:**

A. 0

B. 1

C. -1

D. 2

**Solution:**

**Ques No 14:**

In a triangle ABC, if a, b, c are in AP, then find the value of tan(A/2)tan(C/2).

**Options:**

A. 1/4

B. 1/3

C. 1/2

D. 1/5

**Solution:**

**Ques No 15:**

In a triangle ABC, if bsinC(b cosC + c cosB) = 42, then the area of the triangle ABC is

**Options:**

A. 21 sq. units

B. 42 sq. units

C. 20 sq. units

D. None of these

**Solution: **

Read : Trigonometric Allied Angles Important Questions

**Ques No 16:**

In a triangle ABC, if b = 3, c = 5 and cos(B – C) = 7/25, then find the value of tan(A/2).

**Options:**

A. 1/3

B. 1/4

C. 1/2

D. None of these

**Solution:**

**Ques No 17:**

In a triangle ABC, x = tan{(B – C)/2}tan{A/2}, y = tan{(C – A)/2}tan{B/2}, z = tan{(A – B)/2}tan{C/2}, then

**Options:**

A. x + y + z = 0

B. x + y + z = -xyz

C. x + y + z = xyz

D. None of these

**Solution:**

**Ques No 18:**

The sides of a triangle ABC are a, b, , then the greatest angles of the triangle ABC is

**Options:**

A. 135 degree

B. 105 degree

C. 120 degree

D. 150 degree

**Solution:**

**Ques No 19:**

In a triangle ABC, the value of is

**Options:**

A. 1

B. 4

C. 3

D. 2

**Solution:**

**Ques No 20:**

In a triangle ABC, the value of is

**Options:**

A. (a + b)/c

B. c/(a – b)

C. c/(a + b)

D. (a – b)/c

**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 |