Quantitative Aptitude

Geometry

1,950 Questions
All Circle Tangents and Chords 772 Coordinate Geometry 360 Circle and Arc Measures 216 Triangle Centers and Medians 175 Composite and Inscribed Shapes 174 Similarity, Congruence, and Proportionality 118 Right Triangles and Pythagorean Theorem 100 Standard 2D Mensuration 22 Polygon and Angle Sums 10 3D Solid Mensuration 3

Geometry Questions

Multiple choice

P is a point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersects the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is

  1. 5 cm

  2. 4 cm

  3. 4.5 cm

  4. 5.5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let O be the center, P the external point. OP = 13. Secant PAB, PA = 9, AB = 7, so PB = 16. Power of point P = PA * PB = 9 * 16 = 144. Also, Power = d^2 - r^2, where d=13. 144 = 13^2 - r^2 = 169 - r^2. r^2 = 169 - 144 = 25. r = 5.

Multiple choice

From a point P, a tangent is drawn to a circle. If the length of the tangent is 3 cm and the distance of point P from the centre of the circle is 5 cm, find the radius of the circle.

  1. 3 cm

  2. 4 cm

  3. 5 cm

  4. 6 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The tangent to a circle is perpendicular to the radius at the point of contact. This forms a right triangle with the radius (r), tangent (3 cm), and hypotenuse (5 cm). r^2 + 3^2 = 5^2, so r^2 = 25 - 9 = 16, r = 4 cm.

Multiple choice

The radius of the circle in which an isosceles triangle of sides 20 cm, 20 cm and 24 cm can be inscribed is

  1. 12 cm

  2. 15 cm

  3. 13 cm

  4. 12.5 cm

  5. 17 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For an isosceles triangle with sides 20, 20, 24, the height h to the base 24 is sqrt(20^2 - 12^2) = sqrt(400 - 144) = sqrt(256) = 16. Area = 0.5 * base * height = 0.5 * 24 * 16 = 192. Circumradius R = (abc) / (4 * Area) = (20 * 20 * 24) / (4 * 192) = 9600 / 768 = 12.5.

Multiple choice

The locus of points 4 cm away from a fixed point M is _________.

  1. an angle bisector

  2. a circle with diameter 4 cm and centre M

  3. a straight line

  4. a circle with radius 4 cm and centre M
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The locus of points at a constant distance from a fixed point is the definition of a circle with that point as the center and the distance as the radius.

Multiple choice

If the hypotenuse of a right angled triangle is 6 cm longer than the shortest leg and the longer leg is 3 cm more than the shortest leg, find the length of the shortest leg.

  1. 14 cm

  2. 12 cm

  3. 10 cm

  4. 9 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the shortest leg be x. Hypotenuse = x + 6, longer leg = x + 3. By Pythagoras: x^2 + (x + 3)^2 = (x + 6)^2. Solving x^2 + x^2 + 6x + 9 = x^2 + 12x + 36 gives x^2 - 6x - 27 = 0. Factoring (x - 9)(x + 3) = 0, so x = 9.

Multiple choice

The area of a circle inscribed in a square of side 28 cm is

  1. 570 cm2

  2. 1968 cm2

  3. 616 cm2

  4. 4464 cm2

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A circle inscribed in a square has a diameter equal to the side of the square. Diameter = 28 cm, so radius = 14 cm. Area = pi * r^2 = (22/7) * 14 * 14 = 22 * 2 * 14 = 616 cm^2.