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Question
In Fig., if AB = AC, prove that BE = EC
Solution
Since tangents from an exterior point to a circle are equal in length.
∴ AD = AF [Tangents from A]
BD = BE [Tangents from B]
CE = CF [Tangents from C]
Now,
AB = AC
⇒ AB – AD = AC – AD [Subtracting AD from both sides]
⇒ AB – AD = AC – AF [Using (i)]
⇒ BD = CF ⇒ BE = CF [Using (ii)]
⇒ BE = CE [Using (iii)]
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