Question

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​

Answer 1

Answer:

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Answer 2

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.