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CAT 2006 — QA Question 21

Basics of CirclesEasy
Passage / Data

Answer the following question based on the information given below.

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.

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

  • 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
⇒ ​​​​​​​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).

CAT 2006 QA Q21: A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meet — Solution | TheCATExam