CAT 2006 — QA Question 21
Basics of CirclesEasy
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:
Answer & solution
Correct answer: 50π
- A
32π
50π
- C
40.5π
- D
81π
- E
undeterminable
Solution
Let CB = x cm
In a right triangle if DC is the altitude from right vertex, DC2 = AC × BC
∴ 62 = 2 × x
⇒ âââââââx = 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).