## Twentyfirst SSC CGL level Question Set, 3rd on topic Geometry

This is the twentyfirst question set of 10 practice problem exercise for SSC CGL exam and 3rd on topic Geometry. The questions generally are on circles but involve concepts on triangles and quadrilaterals also.

### Method for taking the test and get the best results from the test set:

**Before start,**go through the three relevant tutorials,**Geometry basic concepts part 1,****Geometry basic concepts part 2,****Geometry basic and rich concepts part 3 on Circles,****Basic and Rich concepts Geometry Part 4 on Arc angle subtending concepts,**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 third tutorial. Don't do the exercise as you are preparing for a hard competitive test. For you, taking the test will involve a different and more stringent method.**Basic and Rich Concepts Geometry Part 5 on Proof of Median relations****Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 12 minutes.**When the time limit of 12 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 12 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.

### Twentyfirst question set- 10 problems for SSC CGL exam: 3rd on Geometry - time 12 mins

### Problem exercise

The recommended time limit is 12 minutes

#### Problem 1.

In a right triangle $\triangle ABC$, the $\angle A = 90^0$ and $AD$ is perpendicular to $BC$. If areas of the triangles $\triangle ABC = 40cm^2$ and $\triangle ACD = 10cm^2$ with $AC = 9cm$, the length of $BC$ is,

- 4cm
- 12cm
- 18cm
- 6cm

#### Problem 2.

If the ratio of an external anglre and an internal angle of a regular polygon is $1 : 17$, the number of sides of the regular polygon is,

- 12
- 36
- 20
- 18

#### Problem 3.

In an isosceles $\triangle ABC$, $AB=AC$. A circle passing through $B$ and touching AC at its middle point, intersects $AB$ at $P$. Then $AP : AB$ is,

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

#### Problem 4.

In $\triangle ABC$, $\angle C$ is an obtuse angle. The bisectors of exterior angles at $A$ and $B$ meet extended $BC$ and $AC$ at $D$ and $E$ respectively. If $AB = AD=BE$ then $\angle ACB$ is

- $105^0$
- $110^0$
- $135^0$
- $108^0$

#### Problem 5.

How many triangles can be formed by taking any three from the four line segments of lengths, 2cm, 3cm, 5cm and 6cm?

- 1
- 2
- 3
- 4

#### Problem 6.

In right $\triangle ABC$, $BL$ and $CM$ are two medians with right angle at $\angle A$ and $BC=5cm$. If $BL = \displaystyle\frac{3\sqrt{5}}{2}$, then the length of $CM$ is,

- $2\sqrt{5}$cm
- $10\sqrt{2}$cm
- $5\sqrt{2}$cm
- $4\sqrt{5}$ cm

#### Problem 7.

In $\triangle ABC$, $D$ and $E$ are two points on the sides $AC$ and $BC$ respectively, such that $DE=18$cm, $CE=5$cm and $\angle DEC = 90^0$. If $tan \angle ABC = 3.6$, then $AC : CD$ is

- $2BC : CE$
- $BC : 2CE$
- $CE : 2BC$
- $2CE : BC$

#### Problem 8.

$AB$ is a chord to a circle and $TAP$ is the tangent to the circle at $A$. If $\angle BAT = 75^0$ and $\angle BAC= 45^0$, where $C$ is a point on the circle, then $\angle ABC$ is,

- $40^0$
- $60^0$
- $70^0$
- $45^0$

#### Problem 9.

If radii of two circles be 6cm and 3cm and the length of the transverse common tangent be 8cm, then the distance between the centers is,

- $\sqrt {140}$cm
- $\sqrt {145}$cm
- $\sqrt {135}$cm
- $\sqrt {150}$cm

#### Problem 10.

Two circles with centers at $P$ and$Q$ intersect each other at $B$ and $C$. Two points on both sides of $C$ are placed such on the circles that $ACD$ are collinear with $A$ on the first circle. If $\angle APB = 130^0$, find $\angle BQD$.

- $130^0$
- $165^0$
- $65^0$
- $15^0$

You may refer to the detailed solution of this question set in **SSC CGL level Solution Set 21, Geometry 3.**

**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**

**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**

**Other SSC CGL level question sets on Geometry are:**

**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 Solution Set 39, Geometry 7**

**SSC CGL level Question Set 39, Geometry 7**

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

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

**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**

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

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

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

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