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CAT 1997 — QA Question 26

Basics of CirclesEasy
Passage / Data

Direction: Answer the questions based on the following information.

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC and 15% watched CNN.

AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm, AC is 12 cm and BD is 9 cm, find the area of the quadrilateral ACBD.

Answer & solution

  • A

    54π sq.cm

  • B

    216π sq.cm

  • C

    162π sq.cm

  • None of these

Solution

Since AB is the diameter of the circle, ∠ACB would be right angle. In this triangle, we know AB = 15 and AC = 12. So we can find BC. Hence, BC = 9. Since BC = BD, AD = AC (similar triangles).
Hence, area of ΔACB = Area of Δ ABD =12 × AC × CB = 12 × 12 × 9 = 54 cm2

So the area of quadrilateral ACBD = 2 × 54 = 108 sq. cm.

CAT 1997 QA Q26: AB is the diameter of the given circle, while points C and D lie on the circumference as shown. If AB is 15 cm — Solution | TheCATExam