Question

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?

• A. DE // BC
  
  
• B. $△ABC$ is equilateral
  
  
• C. DE intersects BC
  
  
• D. None of these

Answer 1

The correct option is A

DE // BC

AB = AC (given, $△ABC$ is isosceles)

Let $\angle ABC=\angle ACB=x^{\circ }$(say)

DA is tangent to the circle (given)

$\angle ABC=\angle BAD=x^{\circ }$ (angle in the alternate segment)

$\therefore DE//BC$ (alternate angles are equal)