CAT 1997 — QA Question 26
Basics of CirclesEasy
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
Correct answer: None of these
- 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 × AC × CB = × 12 × 9 = 54 cm2
So the area of quadrilateral ACBD = 2 × 54 = 108 sq. cm.