## Geometry triangle questions for SSC CGL and other geometry questions Set 80

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### 10 problems on Geometry for SSC CGL Set 8 - answering time 12 mins

#### Problem 1.

The internal bisectors of the $\angle B$ and the $\angle C$ of $\triangle ABC$ intersect at $O$. If $\angle A=100^0$, the $\angle BOC$ is,

- $110^0$
- $140^0$
- $120^0$
- $130^0$

#### Problem 2.

G is the centroid of $\triangle ABC$. The medians AD and BE intersect at right angles. If the lengths of AD and BE are 9 cm and 12 cm respectively, the length of AB (in cm) is,

- 10
- 10.5
- 9.5
- 11

#### Problem 3.

An interior angle of a regular polygon is 5 time its exterior angle. Then the number of sides of the polygon is,

- 16
- 18
- 12
- 14

#### Problem 4.

ABCD is a cyclic trapezium with AB || DC and AB as the diameter. If $\angle CAB=30^0$, then $\angle ADC$ is,

- $120^0$
- $30^0$
- $150^0$
- $60^0$

#### Problem 5.

Two circles with centers P and Q intersect at B and C. A and D are points on the first and second circles respectively, such that A, C and D are collinear. If $\angle APB=130^0$, the value of $\angle BQD$ is,

- $65^0$
- $135^0$
- $130^0$
- $195^0$

#### Problem 6.

AB and AC are tangents to a circle. PQ, another tangent of the circle at the point D on the circle, intersects AB and AC at P and Q respectively. If AB is 15 cm and QA is 9 cm, then DQ is,

- 4.5 cm
- 3 cm
- 7.5 cm
- 6 cm

#### Problem 7.

If two circles of radii 5 cm and 3 cm touch externally, the ratio in which the direct common tangent to the circles divide externally the line joining the centers of the circles is,

- 2.5 : 1.5
- 1.5 : 2.5
- 3 : 5
- 5 : 3

#### Problem 8.

AC is the transverse common tangent to two circles with centers at P and Q and radii 6 cm and 3 cm at the points A and C respectively. If AC cuts PQ at the point B and AB is 8 cm, then the length of PQ is,

- 13 cm
- 15 cm
- 10 cm
- 12 cm

#### Problem 9.

Length of a chord PQ in a circle is 18 cm. AB is the perpendicular bisector of PQ at M and intersects the circle at A and B. If MB = 3 cm, the length of AB is,

- 25 cm
- 27 cm
- 28 cm
- 30 cm

#### Problem 10.

Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the chords is 21 cm. The length of the other chord is then,

- 10 cm
- 12 cm
- 18 cm
- 15 cm

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 80, Geometry 8.**

#### Answers to the 10 questions on Geometry for SSC CGL Set 8

**Problem 1.** Option b: $140^0$.

**Problem 2.** Option a: 10.

**Problem 3.** Option c: 12.

**Problem 4.** Option a: $120^0$.

**Problem 5.** Option c: $130^0$.

**Problem 6.** Option d: 6 cm.

**Problem 7.** Option d: 5 : 3.

**Problem 8.** Option b: 15 cm.

**Problem 9.** Option d: 30 cm.

**Problem 10.** Option c: 18 cm.

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