Question

the incircle of ∆ABC touches the side BC, CA and AB at D, E and F respectively. if AB = AC, prove that BD= CD

Answer 1

BD = CD , if AB = AC & the incircle of ∆ABC touches the side BC, CA and AB at D, E and F respectively

Step-by-step explanation:

the incircle of ∆ABC touches the side BC, CA and AB at D, E and F respectively

Equal Tangents

AF = AE

BF = BD

CD = CE

AB = AC  ( Given)

AB = AF + BF

AC = AE + CE

=> AF + BF = AE + CE

AF = AE

=> BF = CE

CF = BD   & CE = CD

=> BD = CD

QED

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Proved