Triangles(Quantitative Aptitude ) Questions and answers for exam Preparation

Quantitative Aptitude

TRIANGLES MCQs

Total Questions : 83 | Page 7 of 9 pages

Question 61. ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

PB = PC
PB > PC
PB < PC
PB = $$\frac{1}{2}$$ PC

Discuss Question

Answer: Option A. -> PB = PC
here given that = AB = AC
AQ + BQ = AR + RC
we know that
BQ = PB & PC = RC
AQ + PB = AR + PC
also AQ = AR
AR + PB = AR + PC
PB = PC

Question 62. In a ΔABC, ∠A + ∠B = 75° and ∠B + ∠C = 140°, then ∠B is:

40°
35°
50°
45°

Discuss Question

Answer: Option B. -> 35°
∠A + ∠B = 75° . . . . . . (i)
∠B + ∠C = 140° . . . . . (ii)
(we know)
∠A + ∠B + ∠C = 180° . . . . . . (iii)
from equation (i) & (iii)
∠C = 105° . . . . . . . . . . . . . . . (iv)
from equation (ii) & (iv)
∠B = 35°

Question 63. An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is:

$$2\sqrt 3 $$ cm
$$3\sqrt 2 $$ cm
$$4\sqrt 3 $$ cm
$$\sqrt 3 $$ cm

Discuss Question

Answer: Option A. -> $$2\sqrt 3 $$ cm
$$\eqalign{
& R = \frac{a}{{\sqrt 3 }} \cr
& R = \frac{6}{{\sqrt 3 }} \cr
& R = 2\sqrt 3 \,{\text{cm}} \cr} $$

Question 64. ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, AC respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is:

Equilateral
Isosceles triangle
Right angle triangle
None of these

Discuss Question

Answer: Option A. -> Equilateral
Given in question AD = BE = CF
[DB = AF = EC] Because
AB = BC = CA
So, Triangle is equilateral

Question 65. ΔABC is similar to ΔDEF. If the sides of ΔABC, that is AB, BC and CA, are 3, 4 and 5 cms respectively, what would be the perimeter of the ΔDEF, if the side DE measures 12 cms ?

24 cms
30 cms
36 cms
48 cms

Discuss Question

Answer: Option D. -> 48 cms
Perimeter of ΔABC
= 3 + 4 + 5
= 12
$$\eqalign{
& \frac{{{\text{Perimeter}}\,{\text{of}}\,\vartriangle ABC}}{{{\text{Perimeter}}\,{\text{of}}\,\vartriangle DEF}} = \frac{{AB}}{{DE}} \cr
& \frac{{12}}{{{\text{Perimeter}}\,{\text{of}}\,\vartriangle DEF}} = \frac{3}{{12}} \cr} $$
Perimeter of ΔDEF = 48 cms

Question 66. In ΔPQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be

5 : 11
6 : 5
11 : 6
11 : 5

Discuss Question

Answer: Option A. -> 5 : 11
∵ ΔPQR ∼ ΔPXY
$$\eqalign{
& \frac{{PX}}{{PQ}} = \frac{{XY}}{{QR}} \cr
& \frac{5}{{\left( {5 + 6} \right)}} = \frac{{XY}}{{QR}} \cr
& XY:QR = 5:11 \cr} $$

Question 67. The side BC of a triangle ABC is proceed to D. If ∠ACD = 112° and ∠B = $$\frac{3}{4}$$ ∠A, then the measure of ∠B is:

64°
30°
48°
45°

Discuss Question

Answer: Option C. -> 48°
Assume, ∠A = x
∴ ∠B = $$\frac{3}{4}$$ x
∠A + ∠B = 112° (∵ sum of two interior angle is equal to the exterior angle of the third angle)
$$\eqalign{
& {x^ \circ } + \frac{3}{4}{x^ \circ } = {112^ \circ } \cr
& \frac{{7{x^ \circ }}}{4} = {112^ \circ } \cr
& {x^ \circ } = {64^ \circ } \cr
& {\text{Hence,}} \cr
& \angle B = \frac{3}{4} \times {64^ \circ } \cr
& \angle B = {48^ \circ } \cr} $$

Question 68. In a ΔPQR, ∠Q = 55° and ∠R = 35°. Find the ratio of angles subtended by side QR on circumcenter, incenter and orthocenter of the triangle.

3 : 2 : 1
3 : 2 : 4
3 : 2 : 4
4 : 3 : 2

Discuss Question

Answer: Option D. -> 4 : 3 : 2
Circumcenter at the mid point of QR hence angle made by QR
= 2 × 90°
= 180°
Angle made by QR at In center
= 90° + $$\frac{1}{2}$$ × ∠P = 135°
Ortho center is at point 'P'
Hence angle made by QR = 90
Then ration C : I : O
= 180 : 135 : 90
= 4 : 3 : 2

Question 69. In an isosceles triangle ΔABC, AB = AC and ∠A = 80°. The bisector of ∠B and ∠C meet at D. The ∠BDC is equal to.