Question : A 15 cm long perpendicular is drawn from the centre of a circle to its 40 cm long chord. Find the radius of the circle.
Option 1: 25 cm
Option 2: 27 cm
Option 3: 22 cm
Option 4: 20 cm
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Correct Answer: 25 cm
Solution : Given: Chord length = 40 cm The perpendicular distance from centre to chord = 15 cm Let the chord be AB and R be the radius of the circle. Since a perpendicular from the centre divides a chord into two equal parts, AP = 20 cm In $\triangle$OAP Using Pythagoras' theorem: OA 2 = OP 2 + PA 2 . R 2 = 15 2 + 20 2 ⇒ R 2 = 225 + 400 = 625 ⇒ R = 25 Hence, the correct answer is 25 cm.
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