## 37th SSC CGL level Question Set, 5th on topic Geometry

This is the 37th question set of 10 practice problem exercise for SSC CGL exam and 5th on topic Geometry. You need to take this test first before referring to the corresponding solution set. As expected some of the problem pictorial representation seemed to be complex, but once you represent a geometric figure properly even in a quick sketch, rest should not take much time.

### 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,**and**Geometry basic concepts part 2,**or any other short but good material to refresh your concepts if you so require. This question set is in fact the set of exercise problems at the end of the first tutorial. Don't do the exercise as you are preparing for a hard competitive test. For you, taking the test will involve a different more stringent method.**Geometry basic and rich concepts part 3 on Circles****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.

### 37th question set- 10 problems for SSC CGL exam: 5th on Geometry - answering time 15 mins

#### Problem 1.

Two chords AB and CD of a circle with centre at O intersect each other at point P. If the two non-overlapping angles $\angle AOD=100^0$ and $\angle BOC=70^0$ then the value of $\angle APC$ is,

- $80^0$
- $75^0$
- $95^0$
- $85^0$

#### Problem 2.

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the larger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at E. The length of line segment AD is,

- 17 cm
- 19 cm
- 18 cm
- 20 cm

#### Problem 3.

In a $\triangle ABC$, AD is perpendicular dropped on side BC and E is a point on AD so that AE : ED = 5 : 1. If $\angle BAD = 30^0$ and $\tan \angle ACB = 6\tan \angle DBE$, then $\angle ACB$ is,

- $15^0$
- $30^0$
- $45^0$
- $60^0$

#### Problem 4.

In $\triangle ABC$ when the points D and E on sides AB and AC are joined, the line DE turns out to be parallel to BC and also bisects the triangle into two equal areas. Under this condition, the ratio of DB : AB is,

- $1 : 2$
- $\sqrt{2} : 1$
- $(\sqrt{2} - 1) : \sqrt{2}$
- $1 : \sqrt{2}$

#### Problem 5.

The external bisectors of $\angle B$ and $\angle C$ of $\triangle ABC$ with AB and AC extended to E and F respectively, meet at point P. If $\angle BAC=100^0$, then $\angle BPC$ is,

- $40^0$
- $50^0$
- $80^0$
- $100^0$

#### Problem 6.

Angle between the two internal bisectors of angles $\angle B$ and $\angle C$ in $\triangle ABC$ is $120^0$. The $\angle A$ is,

- $20^0$
- $90^0$
- $30^0$
- $60^0$

#### Problem 7.

Two chords AB and CD of a circle with centre O intersect at point P. If $\angle ADP=23^0$ and $\angle APC=70^0$ then $\angle BCD$ is,

- $47^0$
- $45^0$
- $67^0$
- $57^0$

#### Problem 8.

In $\triangle ABC$ AD is the internal bisector of the $\angle A$ meeting the side BC at D. If BD=5 cm and BC=7.5 cm, the ratio of AB : AC is,

- 1 : 2
- 2 : 1
- 4 : 5
- 3 : 5

#### Problem 9.

P and Q are two points on a circle with centre at O. R is a point between P and Q on the minor arc formed by P and Q. If tangents to the circle at P and Q meet at point S with $\angle PSQ = 20^0$, then $\angle PRQ$ is,

- $80^0$
- $100^0$
- $160^0$
- $200^0$

#### Problem 10.

Two circles intersect each other at points A and B. A straight line parallel to AB intersects the two circles consecutively at C, D, E and F. If CD=4.5 cm the length of line segment EF is,

- 4.5 cm
- 9 cm
- 1.5 cm
- 2.25 cm

### Answers to the problems

**Problem 1: **c: $95^0$.

**Problem 2: **b: 19 cm.

**Problem 3: **d: $60^0$.

**Problem 4: **c: $(\sqrt{2} - 1) : \sqrt{2}$.

**Problem 5: **a: $40^0$.

**Problem 6: **d: $60^0$.

**Problem 7: **a: $47^0$.

**Problem 8: **b: 2 : 1.

**Problem 9: **b: $100^0$.

**Problem 10: **a: 4.5 cm.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 37, Geometry 5.**

**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**

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