## Circle questions Cyclic Quadrilateral questions SSC CGL set 20

Solve 10 circle questions cyclic quadrilateral questions for SSC CGL Set 20 in 12 minutes. Verify correctness from answers. Learn to solve from solutions.

Answers and link to the solutions are at the end.

Now set the stopwatch alarm and start taking this test. It is not difficult.

### 10 Circle questions quadrilateral questions SSC CGL Geometry Set 20 - time to solve 12 mins

#### Problem 1.

In a cyclic quadrilateral $ABCD$, side $AB$ is extended to $E$ so that $BE = BC$. If $\angle ADC=70^0$ and $\angle BAD=95^0$ then $\angle DCE$ is,

- $140^0$
- $165^0$
- $120^0$
- $110^0$

#### Problem 2.

The ratio between the number of sides of two regular polygons is $1 : 2$ and the ratio between their interior angles is $2 : 3$. The number of sides of the polygons are respectively,

- 5, 10
- 6, 12
- 7, 14
- 4, 8

#### Problem 3.

The length of the diagonal $BD$ of the parallelogram $ABCD$ is 18cm. If $P$ and $Q$ are the centroids $\triangle ABC$ and $\triangle ADC$ respectively, length of $PQ$ is,

- 4cm
- 12cm
- 6cm
- 9cm

#### Problem 4.

In rhombus $ABCD$, a straight line through $C$ cuts extended $AD$ at $P$ and extended $AB$ at $Q$. If $DP =\displaystyle\frac{1}{2}AB$ the ratio of the lengths of $BQ$ and $AB$ is,

- 1 : 2
- 2 : 1
- 3 : 1
- 1 : 1

#### Problem 5.

$A$, $B$ and $C$ are three points on the circumference of a circle. If $AB = AC = 5\sqrt{2}$cm and $\angle BAC=90^0$ the length of radius is,

- 15cm
- 5cm
- 10cm
- 20cm

#### Problem 6.

If $PN$ is the perpendicular from a point $P$ on the circumference of a circle of radius 7cm to its diameter $AB$ and the length of the chord $PB$ is 12cm, the length of $BN$ is,

- $6\displaystyle\frac{5}{7}$ cm
- $3\displaystyle\frac{5}{7}$ cm
- $12\displaystyle\frac{2}{7}$ cm
- $10\displaystyle\frac{2}{7}$ cm

#### Problem 7.

If the angle subtended by a chord at its center is $60^0$, the ratio between the lengths of the chord and the radius is,

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

#### Problem 8.

$AB$ and $CD$ are two parallel chords of respective lengths 8cm and 6cm on the same side of the center of a circle. The distance between them is 1cm. Then the radiius of the circle is,

- 4cm
- 5cm
- 3cm
- 2cm

#### Problem 9.

$ABCD$ is a trapezium whose side $AD$ is parallel to $BC$. Diagonals $AC$ and $BD$ intersect at $O$. If $AO = 3$, $CO = x - 3$, $BO = 3x - 19$ and $DO = x - 5$, the value(s) of $x$ will be,

- 7, 10
- 7, 6
- 12, 6
- 8, 9

#### Problem 10.

A quadrilateral $ABCD$ circumscribes a circle and $AB=6$cm, $CD=5$cm and $AD=7$cm. The length of side $BC$ is,

- 3cm
- 4cm
- 5cm
- 6cm

### Answers to the Circle questions quadrilateral questions SSC CGL Set 20

**Problem 1: **a: $140^0$.

**Problem 2: **d: 4, 8.

**Problem 3: **c: 6cm.

**Problem 4: **b: 2 : 1.

**Problem 5: **b: 5cm.

**Problem 6: **d: $10\displaystyle\frac{2}{7}$ cm.

**Problem 7: **a: 1 : 1.

**Problem 8: **b: 5cm.

**Problem 9: **d: 8, 9.

**Problem 10: **b: 4cm.

Detailed solutions to these questions are available in **SSC CGL level Solution Set 20, Geometry 2.**

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