Question

In the adjoining figure, points A, B, C and D lie on the circle, AD = 24 and BC = 12. What is the ratio of the area of triangle $\Delta$ CBE to that of the triangle $\Delta$ ADE?

• A. 1:4
• B. 1:2
• C. 1:3
• D. data insufficient

Answer 1

The correct option is A 1:4

(b) In $\Delta$ CBE and $\Delta$ ADE

CBA = CDA

(a chord of a circle subtends equal angle an all its circumference)

Similarily BCD = BAD and BEC = AED

(opp. angles)

Therefore $\Delta$ CBE $\Delta$ ADE (AAA similarity rule)

Now Thus, ratios of areas = 1:4,

since Ratio of Areas of 2 similar triangles = Ratio of squares of the corresponding sides