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- TL;DR 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:
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?
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:
From Thales' Theorem (indirectly) we have that ##AF=FM=FD##
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?
Thanks guys.