Circle Property 2 - PS

[karthikpandian19]

In the circle shown in picture, AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE?

(refer the details in the picture)

(A) 6 (B) 7.5(C) 8(D) 9(E) 10

[Anurag@Gurome]

In the circle shown in picture, AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE?

(refer the details in the picture)

(A) 6 (B) 7.5(C) 8(D) 9(E) 10

angle BAC = angle EAD (vertically opposite angles)
angle EBC = angle CDE (formed by the same arc CE)
Since 2 corresponding angles of the triangles CAB and DAE are congruent, that means the 2 triangles are similar. Hence, their sides will be in proportion.

DE/BC = AD/BA
DE/6 = 6/4
DE = 9

The correct answer is D.