In the adjoining figure- points A- B- C and D lie on the circle- A D-24 and B C-12- What is the ratio of the area of triangle - C B E to that of the triangle - ADE - CAT 1997A- 1-4B- 1- 2C- 1- 3D- data insufficient

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In the adjoin...

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 $Δ$ CBE to that of the triangle $Δ$ ADE ? (CAT 1997)

1:4

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1:2

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1:3

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data insufficient

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Solution

The correct option is A 1:4
(b) In $Δ$ CBE and $Δ$ ADE

CBA = CDA

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

Similarily BCD = BAD and BEC = AED

(opp. angles)

Therefore $Δ$ CBE $Δ$ ADE (AAA similarity rule)

Now $\frac{B C}{D A} = \frac{12}{24} = \frac{1}{2}$ Thus, ratios of areas = 1:4,

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

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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 ΔCBE to that of the triangle ΔADE ? (CAT 1997)

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 $Δ$ CBE to that of the triangle $Δ$ ADE ? (CAT 1997)