$ABCD$ is quadrilateral inscribed in a circle $\Gamma$ .Lines $AB$ and $CD$ intersect at $E$ and lines$AD$ and $BC$ intersect at $F$. Prove that the circle with diameter $EF$ and circle $\Gamma$ are orthogonal.
Problem
Source: MMC 2013
Tags: geometry proposed, geometry
jayme
31.05.2013 13:38
Dear Mathlinkers, we can think to the Bodenmiller theorem... Sincerely Jean-Louis
proglote
31.05.2013 18:44
Let $T$ denote the intersection of the diagonals. The projection $F'$ of $F$ onto $ET$ is the inverse of $F$ w.r.t. $\Gamma$, so if $\Gamma = (O, r)$, we have $OF \cdot OF' = r^2$, i.e. the two circles are orthogonal.
Davidinci
13.11.2013 18:57
Why $ F' $ is inverse of $ F $ with respect $ \Gamma $ , Can someone explain me ?
AndrewPie
14.02.2020 11:02
ahhhhhhhhhh, can't solve it
AndrewPie
14.02.2020 11:08
Is the picture like this tho file:///Users/anzhi/Desktop/Screenshot%202020-02-14%20at%204.08.04%20PM.png