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) * (R-OI) = R^2-OI^2
By Euler's theorem the distance OI between incenter and circumcenter is OI^2= R * (R-2r).
PI * IQ = 2rR
Edited on January 31, 2018, 6:48 am
Posted by armando
on 2018-01-31 06:44:55