# Geometry

### There are 24 equally spaced points lying on the circumference of a circle

There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?

1. 4
2. 6
3. 8
4. 12

### How many diagonals can be drawn by joining the vertices of an octagon

How many diagonals can be drawn by joining the vertices of an octagon?

1. 20
2. 24
3. 28
4. 64

### In the figure given, LM is parallel to QR

In the figure given, LM is parallel to QR. If LM divides the triangle PQR such that area of trapezium LMRQ is two times the area of triangle PLM, then what is PL/PQ equal to?

1. 1/3
2. 1/√2
3. 1/√3
4. 1/2

### A circle of radius 10 cm has an equilateral triangle inscribed in it

A circle of radius 10 cm has an equilateral triangle inscribed in it. The length of the perpendicular drawn from the centre to any side of the triangle is

1. 5√3 cm
2. 5 cm
3. 10√3 cm
4. 10 cm

### If A, B, C, D are the successive angles of a cyclic quadrilateral

If A, B, C, D are the successive angles of a cyclic quadrilateral, then what is cos A + cos B + cos C + cos D equal to?

1. 0
2. 1
3. 2
4. 4

### What is the length of the perpendicular drawn from the centre

What is the length of the perpendicular drawn from the centre of circle of radius r on the chord of length √3r?

1. r/4
2. r/2
3. √2r
4. r

### ABC is an isosceles triangle such that AB = BC = 8 cm

ABC is an isosceles triangle such that AB = BC = 8 cm and ∠ABC = 90°. What is the length of the perpendicular drawn from B on AC?

1. 4√2 cm
2. 4 cm
3. 2 cm
4. 2√2 cm

### In the figure given, ∠B = 38°, AC = BC and AD = CD

In the figure given, ∠B = 38°, AC = BC and AD = CD. What is ∠D equal to?

1. 26°
2. 28°
3. 38°
4. 52°

### How many degrees are there in an angle which

How many degrees are there in an angle which equals two-third of its complement?

1. 60°
2. 48°
3. 45°
4. 36°

### ABCD is a square. X is the mid-point of AB

ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. Consider the following statements:

1. Triangles ADX and BAY are congruent
2. ∠DXA = ∠AYB
3. DX is inclined at an angle 60° with AY
4. DX is not perpendicular to AY

Which of the above statements are correct?

1. 2, 3 and 4 only
2. 1, 2 and 4 only
3. 1, 3 and 4 only
4. 1 and 2 only

### In the figure given below, M is the mid-point of AB

In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is congruent to the triangle BCM by

1. SAS rule
2. SSS rule
3. ASA rule
4. AAA rule

### ABC is a triangle with AB = BC and D is an interior point

In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.

Consider the following statements:

1. Triangle ADC is an isosceles triangle.
2. D is the centroid of the triangle ABC.
3. Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

### PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35°

In the figure given below, PQ is parallel to RS and PR is parallel to QS, If ∠LPR = 35° and ∠UST = 70°, then what is ∠MPQ equal to?

1. 55°
2. 70°
3. 75°
4. 80°

### PQR is a non-isosceles right-angled triangle, right angled at Q

In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT= PT, then what is ∠RLM equal to?

1. ∠PQT
2. ∠LRM
3. ∠RML
4. ∠QPT

### ∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C

In the figure given below, ∠A = 80° and ∠ABC = 60°. BD and CD bisect angles B and C respectively. What are the values of x and y respectively?

1. 10 and 130
2. 10 and 125
3. 20 and 130
4. 20 and 125

### PQRS is a parallelogram. PA bisects angle P and SA bisects angle S

In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

1. 60°
2. 75°
3. 90°
4. 100°

### ABC is a triangle and D is a point on the side BC. If BC = 12 cm

ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to

1. 5 cm
2. 6 cm
3. 8 cm
4. 9 cm

### Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm

Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is

1. 5.5 cm
2. 5 cm
3. 3.5 cm
4. 3 cm

### Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC

Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is

1. 5/3 square units
2. 5/2√2 square units
3. 5/4 square units
4. 1 square unit

### Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides

Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

1. Square
2. Rectangle, but need not be a square
3. Rhombus, but need not be a square
4. Parallelogram, but need not be a rhombus

### The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is

The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is

1. 20°
2. 40°
3. 50°
4. 60°