## Circle questions triangle questions for SSC CGL Set 21 with answers

Solve 10 circle questions triangle questions for SSC CGL Set 21 in 12 minutes. Verify correctness from answers. Learn to solve quickly from solutions.

Answers and link to the solutions are at the end.

### 10 Circle questions triangle questions for SSC CGL Set 21 - time to solve 12 mins

#### Problem 1.

In a right triangle $\triangle ABC$, the $\angle A = 90^0$ and $AD$ is perpendicular to $BC$. If areas of the triangles $\triangle ABC = 40cm^2$ and $\triangle ACD = 10cm^2$ with $AC = 9cm$, the length of $BC$ is,

- 4cm
- 12cm
- 18cm
- 6cm

#### Problem 2.

If the ratio of an external anglre and an internal angle of a regular polygon is $1 : 17$, the number of sides of the regular polygon is,

- 12
- 36
- 20
- 18

#### Problem 3.

In an isosceles $\triangle ABC$, $AB=AC$. A circle passing through $B$ and touching AC at its middle point, intersects $AB$ at $P$. Then $AP : AB$ is,

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

#### Problem 4.

InĀ $\triangle ABC$, $\angle C$ is an obtuse angle. The bisectors of exterior angles at $A$ and $B$ meet extended $BC$ and $AC$ at $D$ and $E$ respectively. If $AB = AD=BE$ then $\angle ACB$ is

- $105^0$
- $110^0$
- $135^0$
- $108^0$

#### Problem 5.

How many triangles can be formed by taking any three from the four line segments of lengths, 2cm, 3cm, 5cm and 6cm?

- 1
- 2
- 3
- 4

#### Problem 6.

In right $\triangle ABC$, $BL$ and $CM$ are two medians with right angle at $\angle A$ and $BC=5cm$. If $BL = \displaystyle\frac{3\sqrt{5}}{2}$, then the length of $CM$ is,

- $2\sqrt{5}$cm
- $10\sqrt{2}$cm
- $5\sqrt{2}$cm
- $4\sqrt{5}$ cm

#### Problem 7.

In $\triangle ABC$, $D$ and $E$ are two points on the sides $AC$ and $BC$ respectively, such that $DE=18$cm, $CE=5$cm and $\angle DEC = 90^0$. If $tan \angle ABC = 3.6$, then $AC : CD$ is

- $2BC : CE$
- $BC : 2CE$
- $CE : 2BC$
- $2CE : BC$

#### Problem 8.

$AB$ is a chord to a circle and $TAP$ is the tangent to the circle at $A$. If $\angle BAT = 75^0$ and $\angle BAC= 45^0$, where $C$ is a point on the circle, then $\angle ABC$ is,

- $40^0$
- $60^0$
- $70^0$
- $45^0$

#### Problem 9.

If radii of two circles be 6cm and 3cm and the length of the transverse common tangent be 8cm, then the distance between the centers is,

- $\sqrt {140}$cm
- $\sqrt {145}$cm
- $\sqrt {135}$cm
- $\sqrt {150}$cm

#### Problem 10.

Two circles with centers at $P$ and$Q$ intersect each other at $B$ and $C$. Two points on both sides of $C$ are placed such on the circles that $ACD$ are collinear with $A$ on the first circle. If $\angle APB = 130^0$, find $\angle BQD$.

- $130^0$
- $165^0$
- $65^0$
- $15^0$

Learn to solve the questions quickly at,

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

### Answers to the Circle questions triangle questions for SSC CGL Set 21

**Problem 1. Answer:** Option c: 18cm.

**Problem 2. Answer:** Option b: 36.

**Problem 3. Answer:** Option c: 1 : 4.

**Problem 4. Answer:** Option d: $108^0$.

**Problem 5. Answer:** Option b: 2.

**Problem 6. Answer:** Option a: $2\sqrt{5}$cm.

**Problem 7. Answer:** Option b: $\displaystyle\frac{BC}{2CE}$.

**Problem 8. Answer:** Option b: $60^0$.

**Problem 9. Answer:** Option b: $\sqrt{145}$.

**Problem 10. Answer:** Option a: $130^0$.

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