- 212

- 50

- Summary
- Problems following proof of Bragmagupta's Theorem

Brahmagupta's theorem:

A cyclic quadrilateral is orthodiagonal (diagonals are perpendicular) if and only if the perpendicular to a side from the point of intersection of the diagonals bisects the opposite side.

But I don't understand the first step of the proof for the necessary condition from Proof Wiki: Proof of Brahmagupta's Theorem, that is, if the perpendicular bisects the opposite side then the quad is orthodiagonal. It states:

Thanks guys.

A cyclic quadrilateral is orthodiagonal (diagonals are perpendicular) if and only if the perpendicular to a side from the point of intersection of the diagonals bisects the opposite side.

But I don't understand the first step of the proof for the necessary condition from Proof Wiki: Proof of Brahmagupta's Theorem, that is, if the perpendicular bisects the opposite side then the quad is orthodiagonal. It states:

I've looked at Thale's theorem but do not understand how we can initially state that ##AF=FM=FD## and I was wondering if someone could help me with this?From Thales' Theorem (indirectly) we have that ##AF=FM=FD##

Thanks guys.