## Difficult circle geometry problems with answers

Solve difficult circle geometry problems in SSC CGL 39 within 15 minutes. Verify your solutions from answers. Learn how to solve quickly from solutions.

Answers and link to solutions are at the end.

### Solve 10 difficult circle geometry and other geometry problems in SSC CGL Set 39 - 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 difficult circle geometry and other geometry problems in SSC CGL Set 39

**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: $50^0$.

To know how you can solve these problems quickly, go through the solutions at,

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

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