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

This is the 5th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 2nd on topic Geometry.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through the solutions, one must solve many problems in a systematic manner using the conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

### Method for taking the test and get the best results from the test set:

**Before start,**go through the**tutorials on****Geometry basic concepts part 1 on points lines and triangles ,****Geometry basic concepts part 2 on Quadilaterals 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,****Basic and rich geometry concepts part 5 on proof of median relations,****Basic and rich Geometry concepts part 6 on proof of triangle area from medians,**or any other short but good material to refresh your concepts if you so require.**Basic and Rich Geometry concepts part 7 on laws of sines and laws of cosines****Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.**When the time limit of 15 minutes is over,**mark up to which you have answered,**but go on to complete the set.****At the end,**refer to the answers given at the end to mark your score at 15 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

Now set the stopwatch alarm and start taking this test. It is not difficult.

### 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**

**Related resources that should be useful for you**

**You may refer to:**

* 7 steps for sure success in SSC CGL tier 1 and tier 2 competitive tests* or

*to access all the valuable student resources that we have created specifically for SSC CGL, but*

**section on SSC CGL****generally for any hard MCQ test.**

**Concept tutorials for SSC CGL and other competitive exams on Geometry**

**Basic and rich Geometry concepts part 7, Laws of sines and cosines**

**Basic and rich Geometry concepts part 6, proof of triangle area from medians**

**Basic and rich Geometry concepts part 5, proof of median relations**

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

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

**Geometry, basic concepts part 2, Quadrilaterals polygons and squares**

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

**How to solve difficult Geometry problems quickly in a few steps**

**How to solve intriguing SSC CGL level Geometry problem in a few steps 4**

**How to solve difficult SSC CGL Geometry problems in a few steps 3**

**How to solve difficult SSC CGL Geometry problems in a few steps 2**

**How to solve difficult SSC CGL Geometry problems in a few steps 1**

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