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 $θ$ .
.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 60

Join AD. As AB is the diameter angle ADB = 90. And hence triangle 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, $∠$ AED = 60. Hence option (b)

Suggest Corrections

Similar questions

Q. 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\)
.

In given figure $A B$ is a diameter of a circle. $C D$ is a chord equal to the radius of the circle. $A C$ and $B D$ when extended intersect at a point $E$ . Prove that $∠$ AEB= $60^{\circ}$ .

In the figure, AB is the diameter and AC is a chord of a circle such that ∠BAC = 30^o. The tangent at C intersects AB produced at D. Find /BDC.

In the given figure, AB is a diameter and AC is a chord of the circle and the tangent at C intersects AB produced in D. If $∠ B A C = 30^{\circ}$ , then $∠ C D B =$ ______.