Question

In triangle ABC AB = AC if the interior triangle of ABC touches the side ab BC and CA and ab respectively show that AX = 1/2 of perimeter of triangle ABC​

Answer 1

according according to the question first we will make a triangle ABC then will extend ab side Tu to point y and AC side to point z

when we have to draw circle between ay and az

now

p is a point lying on BC

so w we know that the the two tangent drawn from an external point are always equal

so show A y = a z__________1

now

perimeter perimeter of triangle ABC

AB+BC+AC=AB+CZ++BY

(tangent tangent and bp are equal

similarly similarly tangent CP and seasonal equal)

so perimeter traingle ABC = AY+AZ

(we Vinod that tangent A y andA z are equal

drawn from an exterior point )

so perimeter triangle ABC=2AX

perimeter of triangle ABC/2=AX

hence proved