## Inradius circumradius circle triangle questions SSC CGL Set 36

Solve 10 inradius circumradius circle triangle questions for SSC CGL Set 36 in 15 minutes. Verify correctness from answers. Learn to solve from solutions.

Answers and link to the solutions are at the end.

### 10 Inradius Circumradius Circle Triangle Questions SSC CGL Set 36 - answering time 15 mins

#### Problem 1.

The radius of the circumcircle of a right angled triangle is 15 cm and the radius of the inscribed circle is 6 cm. Then the length of the three sides (in cm) are,

- 30, 24, 25
- 24, 36, 20
- 18, 24, 30
- 30, 40, 41

#### Problem 2.

A chord $AB$ of a circle of radius $(\sqrt{3} + 1)$ cm touches a second concentric circle of radius $(\sqrt{3} - 1)$ cm. The length of $AB$ (in cm) is,

- $2\sqrt[4]{3}$
- $4\sqrt{3}$
- $8\sqrt{3}$
- $4\sqrt[4]{3}$

#### Problem 3.

If the inradius of an equilateral triangle be 5 cm, its circumradius (in cm) is,

- 10
- 15
- 25
- 30

#### Problem 4.

In isosceles $\triangle ABC$ right-angled at B, DP and DQ are two perpendiculars dropped from a point D inside the triangle on the two sides AB and AC such that P and Q lie on AB and AC respectively. If $AP = a$ cm, $AQ=b$ cm and $\angle BAD=15^0$, then $\sin 75^0$ is,

- $\displaystyle\frac{a}{2b}$
- $\displaystyle\frac{2b}{\sqrt{3}a}$
- $\displaystyle\frac{\sqrt{3}a}{2b}$
- $\displaystyle\frac{2a}{\sqrt{3}b}$

#### Problem 5.

Sides of a right-angled triangle are in the ratio 4 : 5 : 6. If the in-radius of the triangle is 3 cm, the altitude of the triangle with base as the largest side is,

- 7.5 cm
- 6 cm
- 8 cm
- 10 cm

#### Problem 6.

Inside a square $\square ABCD$, $\triangle BCE$ is an equilateral triangle. If CE and BD intersect at O, then $\angle BOC$ is equal to,

- $75^0$
- $60^0$
- $90^0$
- $120^0$

#### Problem 7.

$ABCD$ is a rectangle where the ratio of the lengths $AB$ and $BC$ is 3 : 2. If $P$ is the midpoint of $AB$ then the value of $\sin \angle CPB$ is,

- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{3}{4}$
- $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{2}{5}$

#### Problem 8.

The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is,

- 7 cm
- 6 cm
- 5.5 cm
- 8 cm

#### Problem 9.

A square $ABCD$ is inscribed in a circle of unit radius. Semicircles are described externally on each side with the side as the diameter. The area of the region bounded by the semicircles and the circle is,

- 1 sq unit
- 2.5 sq units
- 1.5 sq units
- 2 sq units

#### Problem 10.

A, B and C are three points on a circle such that angles subtended by the chords AB and AC at the centre are non-overlapping $90^0$ and $110^0$ respectively. $\angle BAC$ is then equal to,

- $80^0$
- $90^0$
- $100^0$
- $70^0$

### Answers to the problems

**Problem 1: **c: 18, 24, 30.

**Problem 2: **d: $4\sqrt[4]{3}$.

**Problem 3: **a: 10.

**Problem 4: **c: $\displaystyle\frac{\sqrt{3}a}{2b}$.

**Problem 5: **a: 7.5 cm.

**Problem 6: **a: $75^0$.

**Problem 7: **c: $\displaystyle\frac{4}{5}$.

**Problem 8: **b: 6 cm.

**Problem 9: **d: 2 sq units.

**Problem 10: **a: $80^0$.

For detailed explanation of the solutions clarifying the concepts used for elegant solutions, you should refer to the corresponding **SSC CGL level Solution Set 36, Geometry 4.**

### Guided help on Geometry in Suresolv

To get the best results out of the extensive range of articles of **tutorials**, **questions** and **solutions** on **Geometry **in Suresolv, *follow the guide,*

The guide list of articles **includes ALL articles on Geometry** and relevant topics in Suresolv and **is up-to-date.**