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

Find the radius of a circle, if a chord of length $8$ m is at a distance of $3$ m from the centre of the circle.
  1. $1$ m
  2. $2$ m
  3. $4$ m
  4. $5$ m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This forms a right triangle with the radius as the hypotenuse, half the chord (4 m) as one leg, and the distance from the center (3 m) as the other leg. By the Pythagorean theorem, r = sqrt(4^2 + 3^2) = sqrt(16 + 9) = 5 m.

Multiple choice

Construct a rectangle ABCD of lengh $6$cm and breadth $4$ cm. Construct angle bisectors of $\angle A$ and $\angle B $. Let them meet at O.The distance of O from length AB is:
  1. $3$
  2. $10$
  3. $2$
  4. $8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a rectangle ABCD, the angle bisectors of A and B meet at point O inside the rectangle. Since angle A and angle B are 90 degrees, the bisectors meet at 45 degrees to the base AB. This forms an isosceles triangle ABO with base angles of 45 degrees, making the height of O from AB equal to half the length of AB, which is 6/2 = 3.

Multiple choice

AB, BC and CD are three consecutive sides of a regular polygon. If $\angle BAC = $$20^{\circ}$, Find the number of sides in the polygon
  1. $8$
  2. $7$
  3. $9$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a regular polygon, the angle subtended by a side at the center is 360/n. The angle between two consecutive sides is (n-2)*180/n. The triangle formed by the center and two vertices is isosceles. The angle BAC is 20 degrees. For a regular polygon, the angle subtended by a side at the circumference is 180/n. Here, the angle BAC involves 2 sides, so 2 * (180/n) = 20? No, that's not right. The angle subtended by a side at any point on the circumference is 180/n. If BAC = 20, then 180/n = 20, so n = 9.

Multiple choice

A circle touches the sides $AB$ and $AD$ of a rectangle $ABCD$ at $P$ and $Q$ respectively and passes through the vertex $C$. If the distance of $C$ from chord $PQ$ is $5$ units, then area of the rectangle is :
  1. $45$
  2. $25$
  3. $50$
  4. $75$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the rectangle have sides x and y. The circle passes through C, and touches AB and AD. Using geometry, the distance from C to the chord PQ is related to the dimensions of the rectangle. For a rectangle where a circle touches two sides and passes through the opposite vertex, the area is 25.