In a circle, the length of a chord is 12 cm and the perpendicular distance from the centre of the circle to the chord is 5 cm. What is the radius of the circle? (Rounded up to two decimal places.)

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 05 Jun, 2025 Shift 3)

Answer 1

Given:

Length of the chord = 12 cm

Perpendicular distance from the center of the circle to the chord = 5 cm

Formula Used:

Radius of the circle can be calculated using the relationship between the chord, perpendicular distance, and radius:

\(r^2 = \left(\frac{\text{Chord Length}}{2}\right)^2 + \text{Perpendicular Distance}^2\)

Calculation:

Chord Length / 2 = 12 / 2 = 6 cm

Perpendicular Distance = 5 cm

Substitute values into the formula:

⇒ r² = 6² + 5²

⇒ r2 = 36 + 25

⇒ r2 = 61

Find r:

⇒ r = √61

⇒ r ≈ 7.81 cm

The radius of the circle is approximately 7.81 cm.