## Geometry problems for SSC CGL Set 1

The 10 problems in 1st set of geometry problems for SSC CGL are of different types. Complete the test. Verify from answers. Learn to solve from solution. The 10 problems are generally on triangles and circles.

For best results try to solve all the 10 questions within 12 minutes' time. At the end of this period, score your efforts with 1 mark for every correct answer and minus 0.25 for every wrong one.

You will **find the answers at the end** of the questions.

After taking the test go through the solutions carefully to learn how to solve the questions quickly and correctly from the paired solution set. If needed repeat the test again after some time to check how much you have retained.

**Link to the solution set is also at the end.**

Now set your timer on and start.

### 10 Geometry problems for SSC CGL Set 1 - time to solve 12 mins

#### Problem 1.

$\triangle ABC$ is an isosceles triangle with $AB=AC$ and $AD$ as the median to base $BC$. If $\angle ABC = 35^0$, the $\angle BAD$ is

- $70^0$
- $35^0$
- $55^0$
- $110^0$

#### Problem 2.

In isosceles triangle $\triangle FGH$, $FG \lt 3$ cm and $GH = 8$cm. Then the correct relation is,

- $GH = FH$
- $GH \lt FH$
- $GF = GH$
- $FH \gt GH$

#### Problem 3.

The sum of three altitudes of a triangle is,

- equal to the sum of three sides
- twice the sum of sides
- greater than the sum of sides
- less than the sum of sides

#### Problem 4.

The length of 3 sides of a triangle are, 6cm, 8cm and 10cm. The length of the median to the greatest side is then,

- 5cm
- 8cm
- 4.8cm
- 6cm

#### Problem 5.

$O$ and $C$ are the Orthocenter and the Circumcenter of an acute angled triangle $\triangle PQR$ respectively. The points $P$ and $O$ are joined and produced to meet the side $QR$ at $S$. If $\angle QCR = 130^0$ and $\angle PQS = 60^0$ then $\angle RPS$ is,

- $100^0$
- $35^0$
- $30^0$
- $60^0$

#### Problem 6.

If $I$ is the incenter of $\triangle ABC$, $\angle ABC = 65^0$ and $\angle ACB = 55^0$, the $\angle BIC$ is,

- $110^0$
- $120^0$
- $130^0$
- $140^0$

#### Problem 7.

If the median drawn on the base of a triangle is half its base, the triangle will be,

- acute-angled
- obtuse-angled
- right-angled
- equilateral

#### Problem 8.

In a right angled triangle the product of its two sides equals half of the square of the third side which is the hypotenuse. One of the acute angles must then be,

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

#### Problem 9.

In $\triangle ABC$, two points $D$ and $E$ are taken on the lines $AB$ and $BC$ respectively in such a way that $AC$ is parallel to $DE$. The $\triangle ABC$ and $\triangle DBE$ are then,

- always similar
- always congruent
- similar only if $D$ lies outside the line segment $AB$
- congruent only if $D$ lies outside the line segment $AB$

#### Problem 10.

$AD$ is a median of $\triangle ABC$ and $O$ is the centroid such that $AO = 10cm$. Length of $OD$ (in cm) is,

- 7
- 5
- 4
- 2

### Answers to 10 Geometry problems for SSC CGL Set 1

**Problem 1: **c: $55^0$.

**Problem 2: **a: $GH=FH$.

**Problem 3: **d: less than sum of sides.

**Problem 4: **a: 5cm.

**Problem 5: **b: $35^0$.

**Problem 6: **b: $120^0$.

**Problem 7: **c: right-angled.

**Problem 8: **c: $45^0$.

**Problem 9: **a: always similar.

**Problem 10: **b: 5.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 18, Geometry 1.**

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