In the given figure $△ A B C$ is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

Open in App

Solution

AB = AC (given, $△ A B C$ is isosceles)

Let $∠ A B C = ∠ A C B = x^{\circ}$ (say)

DA is tangent to the circle (given)

$∠ A B C = ∠ B A D = x^{\circ}$ (angle in the alternate segment)

$∴ D E / / B C$ (alternate angles are equal)

Suggest Corrections

Similar questions

In the given figure $△ A B C$ is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

Q. An isosceles triangle ABC is inscribed in a circle with centre O. If

∠ B O C

is right angle, then

∠ A B C

is equal to ___. (Given :

A B = A C

)

Q. An isosceles

△

ABC is inscribed in a circle. If

A B = A C = 12

\sqrt{5} c m

and

B C = 24 c m

, then the radius of the circle is:

In the given figure, $△ A B C$ is an isosceles triangle with $A B = A C$ and $O$ is the centre of the circle. If $∠ A O B = α$ and $∠ A O C = β$ , then which of the following is true?

Q. 55. Isosceles triangle ABC is inscribed in a circle. If AB=AC =25cm , BC=14cm , find the radius of the circle

Join BYJU'S Learning Program

In the given figure △ABC is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

AB = AC (given, △ABC is isosceles) Let ∠ABC=∠ACB=x∘(say) DA is tangent to the circle (given) ∠ABC=∠BAD=x∘ (angle in the alternate segment) ∴DE//BC (alternate angles are equal)

In the given figure $△ A B C$ is isosceles with AB = AC and is inscribed in a circle. If DAE is a tangent to the circle, then which of the following statement is true?

AB = AC (given, $△ A B C$ is isosceles)

Let $∠ A B C = ∠ A C B = x^{\circ}$ (say)

DA is tangent to the circle (given)

$∠ A B C = ∠ B A D = x^{\circ}$ (angle in the alternate segment)

$∴ D E / / B C$ (alternate angles are equal)