Question

Heya!


In the given figure , ABC is a triangle in which AB = AC. Also a circle passing through B and C intersects the sides AB and AC at the points D and E respectively. Prove that AD = AE.
~Thanks in advance! :)

Answer 1

See Below.

Explanation:

We are given that ABC is a triangle in which AB = AC.

A circle passing through B and C also intersects the sides AB and AC at points D and E respectively.

And we want to prove that AD = AE.

By the secant-secant theorem (shown below), we know that:

We are given that AB = AC. So, by substitution:

And by dividing both sides by AB (AB ≠ 0), we acquire:

Q.E.D.