The diameter of the circumcircle passing through I determine the opposite points M N in the circumcircle. Let be O the center of the circumcircle. Then:
PI * IQ = MI * IN (chords theorem) = (R+OI) * (ROI) = R^2OI^2
By Euler's theorem the distance OI between incenter and circumcenter is OI^2= R * (R2r).
So:
PI * IQ = 2rR
Edited on January 31, 2018, 6:48 am

Posted by armando
on 20180131 06:44:55 