Question

The Incircle of ABC touches BC, AC,AB at D,E,F respectively. Let X be a point inside ABC such that the incircle of XBC touches BC, XB,XC at D,Y,Z respectively. Show that E,F,Y,Z are conclycilc

Answer 1

$\mathbb \red{ REFER \: TO \: THE \: ATTACHMENT}$
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This answer was verified by me or rrjack29

✅✅100 per cent correct answer✅✅

We have AF=AE
CD=CE
BF=BD because tangents drawn to the same circle
We'll add them all
AF+CD+BF=AE+CE+BD
substitute the above equations on the RHS
So AF+CD+BF=AF+CE+BD
For the perimeter part u just need to again substitute the values

Answer 2

We have AF=AE
CD=CE
BF=BD because tangents drawn to the same circle
We'll add them all
AF+CD+BF=AE+CE+BD
substitute the above equations on the RHS
So AF+CD+BF=AF+CE+BD
For the perimeter part u just need to again substitute the values

HOPE IT HELPS ✌