LET /\ABC BE ISOSCELES WITH AB=AC,P BE ITS INCENTRE ,GIVEN BC=AB+AP,FIND / BAC

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Dear MITHRESH

In triangle APE

r =AP sinx

In triangle ADB

BD =BC/2 = ABsinx

 BC =2AB sinx

and cosx =(AP +r)/AB

             = AP(1+sinx)/AB

AP = AB cosx/(1+sinx)

given BC =AP +AB

      2AB sinx  = AB cosx/(1+sinx)  +AB

simplyfy

    sinx -cosx =1- 2sin²x

   sinx -cosx = cos2x

square

 1- sin2x = cos²2x

 sin2x= sin²2x

 sin2x=1

 2x=90

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