What is the length (in cm) of the chord of a circle whose radius is 13 cm and whose perpendicular distance from the chord to the centre is 5 cm?

Explanation

Calculation Let AB be the chord and point P be the midpoint of AB, O is the centre Given, OB = 5 cm and OA = 13 cm In ΔOPB Using Pythagoras theorem ⇒ (OB)2 = (OP)2 + (PB)2 ⇒ 132 = 52 + (PB)2 ⇒ PB = √(169 - 25) = 12 As we know, AB = 2 PB AB = 2 × 12 = 24 cm The answer is 24 cm