Question

Not sure what the special point in this problem.

Answer 1

This is what my friend told me, "Let d be the "height drawn from V" of the three lateral faces. The sphere of radius d centred at V touches (tangentially) each of the three sides BC, CA, AB, of the base of the pyramid. Therefore the intersection of the sphere with the plane ABC is the incircle of the triangle ABC. The line VF is perpendicular to the plane ABC, so that F is the centre of that circle. So I reckon that F is the incentre of the triangle."

Answer 2

What does she mean?

Answer 3

@terenzreignz @ParthKohli @Mertsj

Can you help me?