## 39th SSC CGL level Question Set, 7th on topic Geometry

This is the 39th question set of 10 practice problem exercise for SSC CGL exam and 7th on topic Geometry. Some of the problems this time turned out to be not so simple.

### 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 on points lines and triangles ,****Geometry basic concepts part 2 on Quadilaterals Squares Rectangles,****Geometry basic and rich concepts part 3 on Circles,**or any other short but good material to refresh your concepts if you so require.**Basic and rich Geometry concepts part 4 on proof of arc angle subtending concept****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.

### 39th question set- 10 problems for SSC CGL exam: 7th on Geometry - answering time 15 mins

#### Problem 1.

In a rhombus ABCD, AB is produced to F and BA is produced to E such that AB=AE=BF. Then,

- $ED \bot CF$
- $ED \gt CF$
- $ED^2 + CF^2=EF^2$
- $ED || CF$

#### Problem 2.

In a quadrilateral ABCD with unequal sides if the diagonals AC and BD intersect at right angles then,

- $AB^2 + BC^2 = 2(CD^2 + DA^2)$
- $AB^2 + BC^2 = CD^2 + DA^2$
- $AB^2 + CD^2 = BC^2 + DA^2$
- $AB^2 + AD^2 = BC^2 + CD^2$

#### Problem 3.

Two chords AC and BD of a circle with centre at O intersect at right angles at E. If $\angle OAB = 25^0$, then $\angle EBC$ is,

- $15^0$
- $20^0$
- $25^0$
- $30^0$

#### Problem 4.

In a circle of radius 21 cm, an arc subtend an angle of $72^0$ at the centre. The length of the arc is,

- 26.4 cm
- 19.8 cm
- 21.6 cm
- 13.2 cm

#### Problem 5.

A circle with centre at O touches two intersecting lines AX and BY. The two points of contact A and B subtend and angle of $65^0$ at any point C on the major arc of the circle. If P is the point of intersection of the two lines, then the measure of $\angle APO$ is,

- $65^0$
- $25^0$
- $90^0$
- $40^0$

#### Problem 6.

Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED are of lengths 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter is,

- $\sqrt{65}$ cm
- $65$ cm
- $\displaystyle\frac{65}{2}$ cm
- $\frac{1}{2}\sqrt{65}$ cm

#### Problem 7.

I and O are the incentre and circumcentre of $\triangle ABC$ respectively. The line AI produced intersects the circumcircle at point D. If $\angle ABC=x^0$, $\angle BID = y^0$ and $\angle BOD = z^0$, then $\displaystyle\frac{z+x}{y}$ is,

- 1
- 2
- 3
- 4

#### Problem 8.

The radius of two concentric circles are 17 cm and 10 cm. A straight line ABCD intersects the larger circle at A and D and the smaller circle B and C. If BC = 12 cm, then the length of AD is,

- 24 cm
- 34 cm
- 20 cm
- 30 cm

#### Problem 9.

Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to the circles. The relation between PT and PQ is,

- $PT \gt PQ$
- $PT=PQ$
- $PT \lt PQ$
- $PT=2PQ$

#### Problem 10.

O is the circumcentre of triangle ABC. If $\angle BAC = 85^0$ and $\angle BCA = 55^0$, then $\angle OAC$ is,

- $40^0$
- $60^0$
- $50^0$
- $80^0$

### Answers to the questions

**Problem 1.** Option a: $ED \bot CF$.

**Problem 2.** Option c: $AB^2 + CD^2 = BC^2 + DA^2$.

**Problem 3.** Option c: $25^0$

**Problem 4.** Option a: 26.4 cm.

**Problem 5.** Option b: $25^0$.

**Problem 6.** Option a: $\sqrt{65}$ cm.

**Problem 7.** Option b: 2.

**Problem 8.** Option d: 30 cm.

**Problem 9.** Option b: $PT=PQ$.

**Problem 10.** Option c: $50^0$.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 39, Geometry 7.**

**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**

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

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

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

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

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

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

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

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

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

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