Competitive Exams : Quantitative Aptitude - Geometry (Set 3) | Concept of Maths

Question 1

In a cyclic quadrilateral ABCD, the opposite angles are given by $\angle A = 3x - 10^\circ$ and $\angle C = x + 30^\circ$. What is the measure of the angle $\angle A$?

Accepted Answer

C) $110^\circ$

Answer

A) $40^\circ$

Answer

B) $70^\circ$

Answer

D) $150^\circ$

Question 2

A tangent PT is drawn from an external point $P$ to a circle, touching it at $T$. A secant PAB intersects the circle at $A$ and $B$. If $PT = 12cm$ and $PA = 8cm$, find the length of the segment AB.

Accepted Answer

B) 10 cm

Answer

A) 8 cm

Answer

C) 12 cm

Answer

D) 18 cm

Question 3

In $ riangle ABC$, the point $G$ is the centroid. If the area of $ riangle GBC$ is $18cm^2$, what is the total area of $ riangle ABC$?

Accepted Answer

D) $54cm^2$

Answer

A) $36cm^2$

Answer

B) $45cm^2$

Answer

C) $24cm^2$

Question 4

The ratio of an interior angle to an exterior angle of a regular polygon is $7:2$. How many sides does this polygon have?

Accepted Answer

A) 9

Answer

B) 10

Answer

C) 12

Answer

D) 14

Question 5

In $ riangle ABC$, $D$ and $E$ are points on AB and AC respectively such that $DE \parallel BC$. If $\frac{AD}{DB} = \frac{2}{3}$ and $AC = 15cm$, find the length of AE.

Accepted Answer

B) 6 cm

Answer

A) 4 cm

Answer

C) 9 cm

Answer

D) 10 cm

Question 6

Two circles of radii 10 cm and 17 cm intersect each other at two points, and the distance between their centers is 21 cm. What is the length of the common chord?

Accepted Answer

C) 16 cm

Answer

A) 12 cm

Answer

B) 14 cm

Answer

D) 18 cm

Question 7

In $ riangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ intersect at point $O$. If $\angle BAC = 70^\circ$, find the value of $\angle BOC$.

Accepted Answer

B) $125^\circ$

Answer

A) $110^\circ$

Answer

C) $135^\circ$

Answer

D) $145^\circ$

Question 8

The area of two similar triangles $ riangle ABC$ and $ riangle DEF$ are $64cm^2$ and $121cm^2$ respectively. If $EF = 15.4cm$, what is the length of BC?

Accepted Answer

A) 11.2 cm

Answer

B) 12.8 cm

Answer

C) 13.2 cm

Answer

D) 14.4 cm

Question 9

What is the inradius of a right-angled triangle whose base is 15 cm and height is 8 cm?

Accepted Answer

D) 3 cm

Answer

A) 2 cm

Answer

B) 2.5 cm

Answer

C) 4 cm

Question 10

In a circle, two chords AB and CD intersect at a point $E$ inside the circle. If $AE = 6cm$, $EB = 8cm$, and $CE = 4cm$, find the length of ED.

Accepted Answer

A) 12 cm

Answer

B) 10 cm

Answer

C) 16 cm

Answer

D) 9 cm