A 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord. Find the diameter of the circle.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 4)

Answer 1

Given :

A 15 cm long perpendicular is drawn from the centre of a circle to a 40 cm long chord

Concept used :

The line is drawn from the centre of a circle towards a chord always divides the chord in two equal parts and also perpendicular to the chord.

Calculations :

Let the centre of the circle be 'O' and 'OA' = OB is the radius

Let the chord be 'AB' where 'P' is the midpoint of the chord.

The length of chord AC is 40 cm so PA is equal to 20 cm

Now according to the question

OA² = OP² + PB²

OA² = 15² + 20²

OA² = 225 + 400

OA² = 625

⇒ OA = √625

⇒ 25

Now,

Diameter of the circle = 2 × Radius

⇒ 2 × 25

⇒ 50 cm

∴ The diameter of the circle is 50 cm.