## Angle bisector questions and other questions on Geometry with answers

Solve 10 angle bisector questions and other geometry questions for SSC CGL Set 37 in 15 minutes. Verify from answers. Learn to solve from solutions.

Answers and link to the solutions are at the end.

### 10 angle bisector questions and other geometry questions for SSC CGL Set 37 - answering time 15 mins

#### Problem 1.

Two chords AB and CD of a circle with centre at O intersect each other at point P. If the two non-overlapping angles $\angle AOD=100^0$ and $\angle BOC=70^0$ then the value of $\angle APC$ is,

- $80^0$
- $75^0$
- $95^0$
- $85^0$

#### Problem 2.

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the larger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at E. The length of line segment AD is,

- 17 cm
- 19 cm
- 18 cm
- 20 cm

#### Problem 3.

In a $\triangle ABC$, AD is perpendicular dropped on side BC and E is a point on AD so that AE : ED = 5 : 1. If $\angle BAD = 30^0$ and $\tan \angle ACB = 6\tan \angle DBE$, then $\angle ACB$ is,

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

#### Problem 4.

In $\triangle ABC$ when the points D and E on sides AB and AC are joined, the line DE turns out to be parallel to BC and also bisects the triangle into two equal areas. Under this condition, the ratio of DB : AB is,

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

#### Problem 5.

The external bisectors of $\angle B$ and $\angle C$ of $\triangle ABC$ with AB and AC extended to E and F respectively, meet at point P. If $\angle BAC=100^0$, then $\angle BPC$ is,

- $40^0$
- $50^0$
- $80^0$
- $100^0$

#### Problem 6.

Angle between the two internal bisectors of angles $\angle B$ and $\angle C$ in $\triangle ABC$ is $120^0$. The $\angle A$ is,

- $20^0$
- $90^0$
- $30^0$
- $60^0$

#### Problem 7.

Two chords AB and CD of a circle with centre O intersect at point P. If $\angle ADP=23^0$ and $\angle APC=70^0$ then $\angle BCD$ is,

- $47^0$
- $45^0$
- $67^0$
- $57^0$

#### Problem 8.

In $\triangle ABC$ AD is the internal bisector of the $\angle A$ meeting the side BC at D. If BD=5 cm and BC=7.5 cm, the ratio of AB : AC is,

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

#### Problem 9.

P and Q are two points on a circle with centre at O. R is a point between P and Q on the minor arc formed by P and Q. If tangents to the circle at P and Q meet at point S with $\angle PSQ = 20^0$, then $\angle PRQ$ is,

- $80^0$
- $100^0$
- $160^0$
- $200^0$

#### Problem 10.

Two circles intersect each other at points A and B. A straight line parallel to AB intersects the two circles consecutively at C, D, E and F. If CD=4.5 cm the length of line segment EF is,

- 4.5 cm
- 9 cm
- 1.5 cm
- 2.25 cm

### Answers to angle bisector questions and other geometry questions SSC CGL Set 37

**Problem 1: **c: $95^0$.

**Problem 2: **b: 19 cm.

**Problem 3: **d: $60^0$.

**Problem 4: **c: $(\sqrt{2} - 1) : \sqrt{2}$.

**Problem 5: **a: $40^0$.

**Problem 6: **d: $60^0$.

**Problem 7: **a: $47^0$.

**Problem 8: **b: 2 : 1.

**Problem 9: **b: $100^0$.

**Problem 10: **a: 4.5 cm.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 37, Geometry 5.**

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