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.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 50 cm.
Given that
The length of a chord (AB) = 40 cm
Perpendicular length from center to chord (OC) = 15 cm
AC = AB/2 = 40/2 = 20 cm
From the figure, In triangle OAC
OA2 = AC2 + OC2
⇒ OA2 = 202 + 152
⇒ OA2 = 400 + 225
⇒ OA2 = 625
OA = 25 cm
Hence, the diameter of the circle = 2 × OA = 2 × 25 = 50 cm