## 80th SSC CGL level Question Set, 8th on topic Geometry

This is the 80th question set of 10 practice problem exercise for SSC CGL exam and 8th on topic Geometry. You need to take the test first before referring to the corresponding detailed solution set. Some of the problems need suitable strategic approach for quick solution.

The link to the detailed solution to the questions is provided at the end. Going through the solutions is important as the **inner mechanisms of quick problem solving** are clearly described in each solution. This reference is followed by the answers to these questions.

#### Recommended concept tutorials

You may like to go through the **tutorials on,**

**Geometry basic concepts part 1 on points lines triangles, **

**Geometry basic concepts part 2 on Quadrilaterals Squares Rectangles, **

**Geometry basic and rich concepts part 3 on Circles,**

**Basic and rich Geometry concepts part 4 on proof of arc angle subtending concept**

### 80th question set- 10 problems for SSC CGL exam: 8th on Geometry - answering time 15 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 questions

**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.

### Guided help on Geometry in Suresolv

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