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[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.
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Heyatex underline underline bfQuestion 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 an class=

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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:

[tex]AD(AB)=AE(AC)[/tex]

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

[tex]AD(AB)=AE(AB)[/tex]

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

[tex]AD=AE[/tex]

Q.E.D.

Ver imagen xKelvin

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