## 5th SSC CGL Tier II level question Set, 2nd on Geometry

The ten SSC CGL Tier II level questions in this set are specially selected for variety and depth.

These are on,

- circles,
- tangents,
- inscribed rectangle,
- common tangents,
- parallelogram,
- quarter circle,
- medians and more.

For best results,

- this set should be used as a mini-mock test and
- after timed completion and self-scoring from answers,
- the difficulties faced should be cleared up from the corresponding solution set.

*Link of the detailed solutions is at the end.*

Now set the timer and take the test. *By the way don't bother much if you can't solve the questions in 12 minutes scheduled time. That's an ideal. But with intelligent preparation and practice, you can surely reach this level of competence.*

### 5th question set - 10 problems for SSC CGL exam: 2nd on topic Geometry - answering time 15 mins

**Problem 1. **

In figure below, ABCD is a rectangle inscribed inside the circle with centre at O so that ratio of area of the rectangle to the circle is $\sqrt{3} : \pi$.

Line segment CP intersects AB at P. If $\angle OCD=\angle BCP$, ratio of $BP:BC$ equals,

- $1:\sqrt{2}$
- $1:\sqrt{3}$
- $1:2$
- $1:2\sqrt{3}$

**Problem 2.**

In the given figure $O$ is the centre of the circle and A, B, C, and D are four points on the circumference of the circle. Line segments AD and BC intersect at Q so that $\angle AQB=100^0$, while segments CA and DB extended meet at a point P outside the circle and $\angle CPD=60^0$.

The angle $\angle AOB$ is then,

- $60^0$
- $40^0$
- $50^0$
- $55^0$

**Problem 3.**

CD is a common tangent to two circles which intersect each other at points A and B. Then, $\angle CAD+\angle CBD$ is,

- $120^0$
- $360^0$
- $90^0$
- $180^0$

**Problem 4. **

If two equal circles are such that the centre of one lies on the periphery of the other, the ratio of the common chord to the radius of any of the circles is,

- $\sqrt{3}:2$
- $\sqrt{3}:1$
- $\sqrt{5}:1$
- $1:\sqrt{3}$

**Problem 5. **

In the figure below an arc ABC of a circle subtends an angle of $100^0$ at the centre $O$.

If AB is extended to a point D outside the circle, the $\angle CBD$ is,

- $40^0$
- $140^0$
- $50^0$
- $130^0$

**Problem 6.**

In figure below two lines RP and SP touch a circle with centre at O at points A and B respectively and meet at point P.

If the line CD also touches the circle at point Q, then,

- $BP=DP+PC+CD$
- $3BP=DP+PC+CD$
- $4BP=DP+PC+CD$
- $2BP=DP+PC+CD$

** Problem 7.**

In figure below ARBD is a quarter circle of radius 1cm and a second circle is inscribed within the quarter circle touching it at three points.

The radius of the inscribed circle (in cm) is,

- $1-2\sqrt{2}$
- $\displaystyle\frac{\sqrt{2}+1}{2}$
- $\displaystyle\frac{\sqrt{2}-1}{2}$
- $\sqrt{2}-1$

** Problem 8.**

In the figure below P and Q are the mid-points of two sides CD and AD of a rectangle ABCD respectively.

The ratio of areas of $\triangle BPQ$ and rectangle ABCD is,

- $4:9$
- $5:8$
- $8:13$
- $3:8$

**Problem 9.**

In a $\triangle ABC$, two medians AD and CF intersect at G. The ratio of areas of $\triangle DFG$ and the $\triangle ABC$ will then be,

- $1:12$
- $1:9$
- $1:6$
- $1:16$

** Problem 10.**

TP is the common tangent to two circles, the smaller with centre at $O_1$ touching the larger circle it with centre at $O_2$ at point P. The smaller circle is inside the larger one. If TQ is a second tangent to the larger circle at Q and TR is a second tangent to the smaller circle at R, then the ratio $TQ:TR$ is,

- $8:7$
- $7:8$
- $1:1$
- $5:4$

### Answers to the problems

**Problem 1.** **Answer:** b: $1:\sqrt{3}$.

**Problem 2. ****Answer:** b: $40^0$.

**Problem 3.** **Answer:** d: $180^0$.

**Problem 4**. **Answer:** b: $\sqrt{3}:1$.

**Problem 5.** **Answer:** c: $50^0$.

**Problem 6.** **Answer:** d: $2BP=DP+PC+CD$.

**Problem 7.** **Answer:** d: $\sqrt{2}-1$.

**Problem 8.** **Answer:** d: $3:8$.

**Problem 9.** **Answer:** a: $1:12$.

**Problem 10.** **Answer:** c: $1:1$.

**Detailed Solution to this question set**

**SSC CGL Tier II level Solution Set 5, Geometry 2**

### Guided help on Geometry in Suresolv

To get the best results out of the extensive range of articles of **tutorials**, **questions** and **solutions** on **Geometry **in Suresolv, *follow the guide,*

The guide list of articles **includes ALL articles on Geometry** and relevant topics in Suresolv and **is up-to-date.**