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Trigonometry Properties Of Triangle Questions With Solutions (Q No 01 to 20)

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:

In triangle ABC, if \frac{cos A}{a}=\frac{cos B}{b}=\frac{cos C}{c} and a = 2, then area of triangle ABC is

Options:

A. 1

B. 2

C. \sqrt{3}/2

D. \sqrt{3}

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. c2 – 3c – 7 = 0

B. c2 + 3c + 7 = 0

C. c2 – 3c + 7 = 0

D. c2 + 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, sin2A + sin2B + sin2C is

Options:

A. 0

B. 1

C. -1

D. 2

Solution:

Ques No 5:

In c2 = a2 + b2, 2s = a + b + c, then 4s(s – a)(s – b)(s – c) is

Options:

A. s4

B. b2c2

C. c2a2

D. a2b2

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, \frac{2cos A}{a}=\frac{2cos B}{b}=\frac{2cos C}{c}=\frac{a}{bc}+\frac{b}{ca}, 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, \bigtriangleup = a2 – (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. \sqrt{3}

C. 2

D. None of These

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:

If A + B + C = \pi, n \in  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 p1, p2, p3 are altitude of triangle ABC from the vertices A, B, C and \bigtriangleup be the area of the triangle, then p1-1 + p2-1 – p3-1 is

A. (s – a)/\bigtriangleup

B. (s – b)/\bigtriangleup

C. (s – c)/\bigtriangleup

D. s/\bigtriangleup

Solution:

Ques No 14:

In triangle ABC, angle A = 75, angle B = 75, then a + c\sqrt{2} 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, r1, r2, r3 are radius of incircle and excircle, then the value of 1/r1 + 1/r2 + 1/r3 is

A. 1

B. 0

C. 1/r

D. None of These

Solution:

Ques No 17:

If p1, p2, p3 are altitude of triangle ABC from the vertices A, B, C to the opposite sides, then p1p2p3 is

A. (a2b2c2)/R2

B. (a2b2c2)/4R2

C. (4a2b2c2)/R2

D. (a2b2c2)/8R2

Solution:

Ques No 18:

If exradii r1, r2, r3 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 – r1/r2)(1 – r1/r3) = 2, then the triangle is 

A. Right Angled

B. Isosceles

C. Equilateral

D. None of These

Solution:

Ques No 20:

The value of 1/r12 + 1/r22 + 1/r32 + 1/r2  is 

A. 0

B. (a2 + b2 + c2)/\bigtriangleup2

C. \bigtriangleup2/(a2 + b2 + c2)

D. (a2 + b2 + c2)/\bigtriangleup

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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