In Fig., if AB = AC, prove that BE = EC [2 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark

Since tangents from an exterior point to a circle are equal in length.

Therefore, AD = AF ...(i) [Tangents from A]

BD = BE ...(ii) [Tangents from B]

CE = CF ...(iii) [Tangents from C]

Given, AB = AC

$\Rightarrow A B - A D = A C - A D$

[Subtracting AD from both sides]

$\Rightarrow A B - A D = A C - A F$ [Using (i)]

$\Rightarrow B D = C F \Rightarrow B E = C F$ [Using (ii), BE = BD]

$\Rightarrow B E = C E$ [Using (iii), CE = CF]

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