tex] 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! :)

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TheAnimeGirl

High School

Heya!
[tex] \underline{ \underline{ \bf{Question}}}: [/tex] 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! :)

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xKelvin

Answer:
See Below.
Step-by-step 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:
$AD(AB)=AE(AC)$
We are given that AB = AC. So, by substitution:
$AD(AB)=AE(AB)$
And by dividing both sides by AB (AB ≠ 0), we acquire:
$AD=AE$
Q.E.D.
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