## 15th SSC CGL Tier II level Question Set, 4th on Geometry

The ten SSC CGL Tier II level geometry questions in this set are on,

- median ratio at centroid,
- properties of a rhombus,
- properties of diagonals of a parallelogram,
- equilateral triangle,
- angle subtended by an arc of a circle,
- cyclic quadrilateral,
- similar triangles,
- isosceles triangle,
- right angled triangle and much more.

These geometry questions are specially selected for variety and depth with no two questions of same type.

For best results,

- this set should be used as a mini-mock test and
- after timed completion and self-scoring from answers,
- the difficulties faced should be cleared up from the corresponding solution set.

*A few of the problems look simple but deceptively so. In the same way, a few of the problems seem to be quite difficult, but can be solved quickly by identifying key geometric patterns and applying corresponding methods that are based on core concepts. In a few cases, awareness of algebraic patterns and methods becomes important for quick solution.*

**Answers** to the questions, **link to the detailed solutions** and an **useful guide** to how best to take the test are given at the end.

**Preferably** you should go through the **first three tutorials** listed in the guide to refresh your knowledge before going through this mini-mock test.

### 15th SSC CGL Tier II level question set - 10 problems for SSC CGL exam: 4th on topic Geometry - answering time 15 mins

**Problem 1. **

If G is the centroid of an equilateral triangle ABC with side length 10 cm, then the length of AG is,

- $5\sqrt{3}$ cm
- $10\sqrt{3}$ cm
- $\displaystyle\frac{5\sqrt{3}}{3}$ cm
- $\displaystyle\frac{10\sqrt{3}}{3}$ cm

**Problem 2.**

If the ratio of the angles of a quadrilateral is $2:7:2:7$, then the shape

- is a rhombus
- is a parallelogram
- is a trapezium
- cannot be identified

**Problem 3.**

If $D$, $E$ and $F$ are the mid-points of sides $BC$, $CA$ and $AB$ respectively of $\triangle ABC$, then the ratio of the area of the parallelogram $DEFB$ and the area of the trapezium $CAFD$ is,

- $2:3$
- $3:4$
- $1:3$
- $1:2$

**Problem 4. **

If a chord of a circle is equal to its radius, the angle subtended by the chord at the minor arc of the circle is,

- $60^0$
- $150^0$
- $120^0$
- $75^0$

**Problem 5. **

In a cyclic quadrilateral ABCD, AB and DC when extended meet at point P. If PA= 8 cm, PB = 6 cm and PC = 4 cm, the length of PD in cm is,

- 10 cm
- 12 cm
- 6 cm
- 8 cm

**Problem 6.**

In $\triangle ABC$, $DE||BC$ and $AD:DB=5:4$. Then the ratio, $DE:BC$ is,

- $4:5$
- $9:5$
- $5:9$
- $4:9$

** Problem 7.**

In a $\triangle ABC$, $BC=12$ cm. A line CD is drawn to intersect AB at D internally. If $DB=9$ cm, $CD=6$ cm and $\angle BCD=\angle BAC$, ratio of the perimeter of $\triangle ADC$ to that of $\triangle BDC$ is,

- $\displaystyle\frac{5}{9}$
- $\displaystyle\frac{6}{9}$
- $\displaystyle\frac{7}{9}$
- $\displaystyle\frac{8}{9}$

** Problem 8.**

In the figure below, chord $CD$ is parallel to diameter $AB$ of a circle with centre at $O$.

If $\angle CEB=65^0$, then $\angle BCD$ is,

- $25^0$
- $35^0$
- $55^0$
- $45^0$

**Problem 9.**

In $\triangle ABC$, the line $BB_1$ through $B$ intersects side $AC$ at $B_1$. A line through $A$ parallel to $BB_1$ meets $CB$ extended at $A_1$ and another line through $C$ parallel to $BB_1$ meets $AB$ extended at $C_1$. Then which of the following is true?

- $\displaystyle\frac{1}{AA_1}-\displaystyle\frac{1}{CC_1}=\displaystyle\frac{2}{BB_1}$
- $\displaystyle\frac{1}{BB_1}-\displaystyle\frac{1}{AA_1}=\displaystyle\frac{2}{CC_1}$
- $\displaystyle\frac{1}{CC_1}+\displaystyle\frac{1}{AA_1}=\displaystyle\frac{1}{BB_1}$
- $\displaystyle\frac{1}{CC_1}-\displaystyle\frac{1}{AA_1}=\displaystyle\frac{1}{BB_1}$

** Problem 10.**

In an isosceles right $\triangle ABC$, $\angle C=90^0$. If $D$ is any point on $AB$ then $AB^2+BD^2$ is equal to,

- $2CD^2$
- $4CD^2$
- $3CD^2$
- $CD^2$

**Note:** The detailed explanatory solutions are available in the corresponding solution set,

**SSC CGL Tier II level Solution Set 15 on Geometry 4.**

Answers to the questions are given below.

### Answers to the questions

**Problem 1.** Answer: Option d: $\displaystyle\frac{10\sqrt{3}}{3}$ cm.

**Problem 2.** Answer: Option d: cannot be identified.

**Problem 3.** Answer: Option a: $2:3$.

**Problem 4.** Answer: Option b: $150^0$.

**Problem 5.** Answer: Option b: 12 cm.

**Problem 6.** Answer: Option c: $5:9$.

**Problem 7.** Answer: Option c: $\displaystyle\frac{7}{9}$.

**Problem 8.** Answer: Option a: $25^0$.

**Problem 9.** Answer: Option c: $\displaystyle\frac{1}{CC_1}+\displaystyle\frac{1}{AA_1}=\displaystyle\frac{1}{BB_1}$.

**Problem 10.** Answer: Option a: $2CD^2$.

### 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.**