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

The ten SSC CGL Tier II level questions in this set are specially selected for variety and depth with no two questions of same type.

The geometry questions are on,

- area of a triangle,
- laws of sines,
- similar triangles,
- trapezium,
- cyclic quadrilateral,
- circles 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 15 minutes of scheduled time. That's an ideal. But with intelligent preparation and practice, you can surely reach this level of competence or better.*

### 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**

### Guided help on Geometry in Suresolv

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