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# Trigonometry Properties Of Triangle Questions With Solutions (Q No 21 To 40)

Properties of Triangle Questions With Solutions (Q.No. 1 To Q.No 20)
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:

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 r1, r2, r3 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 + r2)

C. ar/(1 – r2)

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:

Ques No 8:

In a right angled triangle ABC, cos2A + cos2B + cos2C 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)
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. r2

C. 1/r

D. 1/r2

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:

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)
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
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