## Geometry SSC CGL: Question set 16 for Tier 2 with answers

Solve 10 questions on Geometry SSC CGL Tier 2 Set 16 in 15 min. Verify from answers. Learn to solve the difficult geometry questions quickly from solutions.

A few of the problems look simple but deceptively so. In the same way, a few of the problems seem to be quite difficult, but can nevertheless be solved quickly by applying strategic rules in geometry problem solving.

Majority of the 10 questions are *Circle questions for competitive exams.*

The **answers to the questions** and the **link to the detailed solutions** are given at the end followed by important related tutorials, question sets and solution sets on Geometry.

### 10 questions on Geometry for SSC CGL Tier 2 Set 16 - answering time 15 mins

**Problem 1. **

If ABCD is a cyclic quadrilateral and AD is its diameter. If $\angle DAC=55^0$, then the value of $\angle ABC$ is,

- $35^0$
- $55^0$
- $125^0$
- $145^0$

**Problem 2.**

AD is perpendicular to the internal bisector of $\angle ABC$ of $\triangle ABC$. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is,

- 3
- 4
- 6
- 8

**Problem 3.**

Among the angles $30^0$, $36^0$, $45^0$ and $50^0$ one angle cannot be an exterior angle of a regular polygon. The angle is,

- $36^0$
- $30^0$
- $50^0$
- $45^0$

**Problem 4. **

The distance between the centres of two circles having radii 8 cm and 3 cm is 13 cm. The length (in cm) of the direct common tangent of the two circles is,

- 15
- 12
- 16
- 18

**Problem 5. **

AB is the diameter of a circle with centre at O. The tangent at C meets AB produced at Q. If $\angle CAB=34^0$, then the value of $\angle CBA$ is,

- $34^0$
- $56^0$
- $124^0$
- $68^0$

**Problem 6.**

Two circles touch each other externally at A. PQ is a direct common tangent to the two circles with P and Q as points of contact. If $\angle APQ=35^0$ then $\angle PQA$ is,

- $75^0$
- $65^0$
- $35^0$
- $55^0$

** Problem 7.**

If $O$ is the circumcentre of a $\triangle ABC$ lying inside the triangle, then $\angle OBC+\angle BAC$ is equal to,

- $90^0$
- $110^0$
- $120^0$
- $60^0$

** Problem 8.**

Three circles of radius 6 cm each touch one another externally. Then the shortest distance from the centre of one circle to the line joining the centres of the other two circles is equal to,

- $6\sqrt{7}$ cm
- $6\sqrt{2}$ cm
- $6\sqrt{5}$ cm
- $6\sqrt{3}$ cm

**Problem 9.**

The point of intersection of the diagonals AC and BD of the cyclic quadrilateral ABCD is P. If $\angle APB=64^0$ and $\angle CBD=28^0$, the value of $\angle ADB$ is,

- $36^0$
- $28^0$
- $32^0$
- $56^0$

** Problem 10.**

A square is inscribed in a quarter circle in such a manner that two of its adjacent vertices lie on two radii at an equal distance from the centre, while the other two vertices lie on the circular arc. If the square has sides of length $x$, then the radius of the circle is,

- $\displaystyle\frac{\sqrt{5}x}{\sqrt{2}}$
- $\sqrt{2}x$
- $\displaystyle\frac{16x}{\pi + 4}$
- $\displaystyle\frac{2x}{\sqrt{\pi}}$

Know **how to apply power strategies for quick solution to difficult geometry problems** from solutions at,

**SSC CGL Tier II level Solution set 16 on Geometry 5.**

### Answers to the questions on geometry for SSC CGL Tier 2 Set 16

**Problem 1.** **Answer:** Option d: $145^0$.

**Problem 2.** **Answer:** Option c: 6.

**Problem 3.** **Answer:** Option c: $50^0$.

**Problem 4.** **Answer:** Option b: 12.

**Problem 5.** **Answer:** Option b: $56^0$.

**Problem 6.** **Answer:** Option d: $55^0$.

**Problem 7.** **Answer:** Option a: $90^0$.

**Problem 8.** **Answer:** Option d: $6\sqrt{3}$ cm.

**Problem 9.** **Answer:** Option a: $36^0$.

**Problem 10.** **Answer:** Option a: $\displaystyle\frac{\sqrt{5}x}{\sqrt{2}}$.

### Guided help on Geometry in Suresolv

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