CAT 1997 — QA Question 42

In ΔBEC and ΔAED

∠CBE = ∠CDE (
angles in the same segment of a circle are equal)
Similarly ∠BCE = ∠EAD (
angles in the same segment of a circle are equal)
∠BEC = ∠AED (Vertical angles are equal) 

∴ By AAA similarity 
ΔCEB ~ ΔAED
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the
corresponding sides

∴ $\frac{area(∆BEC)}{area (∆AED)}={\left(\frac{BC}{DA}\right)}^2={\left(\frac{12}{24}\right)}^2={\left(\frac{1}{2}\right)}^2=\frac{1}{4}$