A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semicircle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm.) will be:
Explanation:
Let CB = x cm
In a right triangle if DC is the altitude from right vertex, DC2 = AC × BC ∴ 62 = 2 × x ⇒ x = 18
⇒ AB = 2 + 18 = 20
∴ Diameter of the semicircle = 20
⇒ Radius of the semicircle = 10
∴ Area = 1/2 × π × 102 = 50π sq. cm.
Hence, option (b).
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