A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle.

Let side BC = 4 cm. Since, the perpendicular to a chord from the centre of the circle bisects the chord, ∴ BM = MC = 2 cm. Given, Diameter = 5 cm, radius = = 2.5 cm. In right ∆OBM, ⇒ OB 2 = BM 2 + OM 2 ⇒ (2.5) 2 = 2 2 + OM 2 ⇒ 6.25 = 4 + OM 2 ⇒ OM 2 = 2.25 ⇒ OM = = 1.5 cm. Similarly in right ∆OAN, ⇒ OA 2 = AN 2 + ON 2 ⇒ (2.5) 2 = 2 2 + ON 2 ⇒ 6.25 = 4 + ON 2 ⇒ ON 2 = 2.25 ⇒ ON = = 1.5 cm. From figure, ⇒ MN = OM + ON = 1.5 + 1.5 = 3 cm. ⇒ AB = DC = MN = 3 cm. ⇒ Area = length × breadth = 4 cm × 3 cm = 12 cm 2 . Hence area of rectangle = 12 cm 2 .

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Mathematics

A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find the area of rectangle.

Circles

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