Question

In the adjoining figure,AB and AC are equal chords of a circle.Line m is parallel to the tangent atpoint A and intersects the chords atpoint D and point E respectively.Prove that AD = AE​

Answer 1

PROOF

1) to prove AD=AE we have to make the diagram which satisfy the the condition which given in the question.

2)after that we have to apply the theorems of the parallel lines which includes the condition of alternate angles.

3) after that we have to apply the theorem of the triangle in which the theorem states that the angle opposite to the equal sides are also equal and vice versa.

4) m║ XY

It is clear that

m║BC

=> BC║XY

we know that

AB = AC

∠1 = ∠2 ( Angle opposite to the equal sides)

hence, BC║XY

∠1 = ∠6

∠2 =∠7 ( Alternate angles)

=> ∠6=∠7 (∠1 = ∠2)

m║XY

∠4 = ∠6

∠5 = ∠7 (Alternate angles)

hence, ∠4 = ∠5 (∠6=∠7)

=> AD = AE (Sides opposite to equal angles are also equal).

For the diagram refer the picture given below.