Question

In the given figure AB is a diameter of the circle, CD is a chord parallel to AB, and AC intersects BD at E. If the ratio of area of triangles AEB and DEC= 4: 1, then find out the value of (\theta\)
.

• A. 30
• B. 60
• C. 45
• D. 15

Answer 1

The correct option is B 60

Join AD. As AB is the diameter $\angle$ ADB = 90. And hence $\Delta$ADB is a right angle triangle.

Triangles AEB and DEC are similar hence if the ratio of area is 4: 1, ratio of sides will be 2:1.

So, AE: DE = 2: 1. In triangle ADE, hypotenuse AE = 2, DE = 1 AD${}^2$ = 4 – 1 = 3. AD = $\sqrt{3}$

So, $\angle$ AED = 60 ${}^{\circ }$ .