Competitive Exams : Quantitative Aptitude - Geometry (Set 2) | Concept of Maths

Question 1

In a cyclic quadrilateral ABCD, the opposite angles are given as $\angle A = (2x + 4)^\circ$ and $\angle C = (4x - 10)^\circ$. What is the measure of $\angle A$?

Accepted Answer

B) $66^\circ$

Answer

A) $60^\circ$

Answer

C) $72^\circ$

Answer

D) $114^\circ$

Question 2

In $ riangle PQR$, the internal bisectors of $\angle Q$ and $\angle R$ meet at point $O$. If $\angle QOR = 124^\circ$, calculate the measure of $\angle P$.

Accepted Answer

C) $68^\circ$

Answer

A) $34^\circ$

Answer

B) $62^\circ$

Answer

D) $56^\circ$

Question 3

Two concentric circles have radii 13 cm and 5 cm. A chord of the larger circle is tangent to the smaller circle. Find the length of this chord.

Accepted Answer

A) 24 cm

Answer

B) 12 cm

Answer

C) 18 cm

Answer

D) 26 cm

Question 4

If the ratio of an interior angle to the exterior angle of a regular polygon is $7:2$, how many sides does the polygon have?

Accepted Answer

D) 9

Answer

A) 7

Answer

B) 8

Answer

C) 10

Question 5

$ riangle ABC \sim riangle DEF$ such that Area($ riangle ABC$) $= 54cm^2$ and Area($ riangle DEF$) $= 24cm^2$. If $BC = 12cm$, find the length of EF.

Accepted Answer

B) 8 cm

Answer

A) 6 cm

Answer

C) 9 cm

Answer

D) 10 cm

Question 6

Chords AB and CD of a circle intersect at a point $P$ inside the circle. If $AP = 8cm$, $PB = 6cm$, and $CP = 4cm$, find the length of PD.

Accepted Answer

C) 12 cm

Answer

A) 8 cm

Answer

B) 10 cm

Answer

D) 14 cm

Question 7

In $ riangle ABC$, AD is the median and $G$ is the centroid. If the length of AG is 8 cm, find the total length of the median AD.

Accepted Answer

A) 12 cm

Answer

B) 10 cm

Answer

C) 16 cm

Answer

D) 24 cm

Question 8

A chord of length 16 cm is drawn in a circle at a perpendicular distance of 6 cm from the center. What is the diameter of the circle?

Accepted Answer

D) 20 cm

Answer

A) 10 cm

Answer

B) 12 cm

Answer

C) 16 cm

Question 9

The diagonals of a rhombus are 16 cm and 12 cm respectively. Calculate the perimeter of the rhombus.

Accepted Answer

B) 40 cm

Answer

A) 32 cm

Answer

C) 48 cm

Answer

D) 56 cm

Question 10

In a circle with center $O$, $\angle OBC = 35^\circ$ where $B$ and $C$ are points on the circumference. Find the angle subtended by arc BC at any point $A$ on the major arc.

Accepted Answer

A) $55^\circ$

Answer

B) $70^\circ$

Answer

C) $35^\circ$

Answer

D) $110^\circ$