Question

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

Answer 1

AD = 24, BC = 12. 

In ΔCBE and ΔADE, 

∠CBA = ∠CDA, ∠BCE = ∠DAE (Angles in the same segment are equal) 

∠BEC = ∠DEA (vertical opposite angles are equal) 

⇒ ΔBCE and ΔDEA are similar Δs with sides in the ratio 1 : 2. 

∴ Ratio of areas = Ratio of square of sides = 12 : 22 = 1 : 4