## 6th SSC CGL Tier II level Question Set, 3rd on Geometry

This is the 6th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 3rd 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 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,****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.

### 6th question set - 10 problems for SSC CGL exam: 3rd on topic Geometry - answering time 15 mins

**Problem 1. **

Lengths of three perpendiculars from a point inside an equilateral triangle on the three sides being 16 cm, 25 cm and 28 cm, the area of the triangle (in cm$^2$) will be.

- $1587\sqrt{3}$
- $1587$
- $2116$
- $2116\sqrt{3}$

**Problem 2.**

If the ratio of sines of angles of a triangle is $1:1:\sqrt{2}$, the ratio of square of the greatest side to sum of the squares of the other two sides is,

- 1:2
- 1:1
- 2:1
- 3:4

**Problem 3.**

The perimeters of similar triangles $\triangle ABC$ and $\triangle PQR$ are 24 cm and 36 cm respectively. If $AB=10$ cm, then $PQ$ (in cm) is,

- 18
- 12
- 15
- 16

**Problem 4. **

In $\triangle ABC$, the bisector of $\angle A$ is AP and it meets BC at P. If a line DE intersects AB, AP and AC at D, Q and E respectively and is perpendicular to AP, then which of the following is true?

- AQ=QP
- AD=AE
- BP=PC
- QP=EC

**Problem 5. **

In a quadrilateral ABCD, $\angle B=90^0$, and $AD^2=AB^2+BC^2+CD^2$. Then the $\angle ACD$ is,

- $45^0$
- $60^0$
- $50^0$
- $90^0$

**Problem 6.**

In figure below the lengths of the four sections of the two diagonals of a trapezium ABCD, namely, AO, BO, CO and DO are given.

Find the possible values of $x$.

- 6, 8
- 8, 9
- 9, 7
- 7, 8

** Problem 7.**

In figure below $\angle AEB=35^0$ and $\angle ADF=75^0$.

The $\angle AFD$ is,

- $65^0$
- $45^0$
- $35^0$
- $55^0$

** Problem 8.**

In the figure below, $O$ is the centre of a circle with $\angle COD=106^0$ and AC as the diameter.

Find $\angle ABD$.

- $55^0$
- $40^0$
- $37^0$
- $43^0$

**Problem 9.**

In the following figure, two circles with centres at P and Q and each of radius 1 cm touch each other at O which is the centre of a third circle of radius 2 cm. The fourth circle with centre at R touches all the three circles.

The radius of the smallest fourth circle (in cm) is,

- $5$
- $\displaystyle\frac{2}{3}$
- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{3}{7}$

** Problem 10.**

In a $\triangle ABC$, $AB=3$ cm, $BC=6$ cm and $CA=5$ cm. Bisector of $\angle A$ meets BC at D. The length of BD is,

- 2.25 cm
- 2 cm
- 2.5 cm
- 3 cm

### Answers to the questions

Problem 1. **Answer:** a: $1587\sqrt{3}$.

Problem 2. **Answer:** b: 1:1.

Problem 3. **Answer:** c: 15.

Problem 4. **Answer:** b: AD=AE.

Problem 5. **Answer:** d: $90^0$.

Problem 6. **Answer:** b: 8, 9.

Problem 7. **Answer:** a: $65^0$.

Problem 8. **Answer:** c: $37^0$.

Problem 9. **Answer:** b: $\displaystyle\frac{2}{3}$.

Problem 10. **Answer:** a: 2.25 cm.

**Detailed Solution to this question set**

**SSC CGL Tier II level Solution Set 6, Geometry 3**

**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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