A chord AB of length 24 cm is drawn in a circle of radius 13 cm. Find the area of the shaded portion APB.
Explanation:
Area of sector O-APB = (x/360) × π × (13)2 = 169πx/360 cm2 Let the perpendicular from O to AB meet AB at M. Hence, OM is the perpendicular bisector of AB. Hence, AM = 24/2 = 12 cm and OM = 5 cm (5, 12, 13 form a pythagorean triplet in right triangle OAM). ∴ Area of triangle OAB = (1/2) × OM × AB = (1/2) × 5 × 24 = 60 cm2 ∴ Required area = [(169πx/360) − 60] cm2 Hence, option (c).
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