## 16th SSC CGL Tier II level Question Set, 5th on Geometry

This is the 16th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 5th on topic Geometry.

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.

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.

### 16th question set - 10 problems for SSC CGL exam: 5th on topic Geometry - 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,

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

**Note:** You should refer to the detailed solution set by clicking on the link below to know **how to apply power strategies for quick solution to difficult geometry problems**,

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

### Answers to the questions

**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: $\displaystyle\frac{\sqrt{5}x}{\sqrt{2}}$.

**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**

**SSC CGL Tier II level question sets and solution sets on Geometry**

**SSC CGL Tier II level Solution Set 16, Geometry 5**

**SSC CGL Tier II level Question Set 16, Geometry 5**

**SSC CGL Tier II level Solution Set 15, Geometry 4**

**SSC CGL Tier II level Question Set 15, Geometry 4 **

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

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

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

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

**SSC CGL Tier II level Solution Set 4, Geometry 1**

**SSC CGL Tier II level Question Set 4, Geometry 1**

#### SSC CGL level question sets and solution sets on Geometry

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**SSC CGL level Question Set 80, Geometry 8**

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**SSC CGL level Solution Set 38, Geometry 6**

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**SSC CGL level Solution Set 37, Geometry 5**

**SSC CGL level Question Set 37, Geometry 5**

**SSC CGL level Solution Set 36, Geometry 4**

**SSC CGL level Question Set 36, Geometry 4**

**SSC CGL level Solution Set 21, Geometry 3**

**SSC CGL Level Question Set 21, Geometry 3**

**SSC CGL level Solution Set 20, Geometry 2**

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**SSC CGL level Solution Set 18, Geometry 1**

**SSC CGL Level Question Set 18, Geometry 1**

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