## Geometry for SSC CGL Tier 2 Set 15 with answers

10 geometry questions for SSC CGL Tier 2 Set 15 are on median ratio, rhombus, parallelogram, circles and more. Solve in 15 mins and verify from answers.

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.

### Geometry questions for SSC CGL tier 2 set 15 - 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 Geometry questions for Tier 2 Set 15

**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.**