28. In the figure, the circle touches the sides AB,BC,AC of AABC at D.E and F
respectively. If AB = AC. prove that BE = EC
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Given: AB = AC
RTP: BE = BC
Proof: We know that tangents to a circle from the same external point are equal in length,
Hence, AD = AF ... (1)
CF = CE ... (2)
BD = BE ... (3)
Now, given that AB = AC,
Therefore, AB - AD = AC - AD [Subtracting AD from both sides]
=> AB - AD = AC - AF [From (1)]
=> BD = CF
=> BE = CE [From (2)]
Therefore, proved.
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