MathDB

7.2

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 7. 2 IK / IO= r / R

Source:

6/7/2020
A non-equilateral triangle ABCABC is inscribed in a circle Γ\Gamma with centre OO, radius RR and its incircle has centre II and touches BC,CA,ABBC,CA,AB at D,E,FD,E, F, respectively. A circle with centre II and radius rr intersects the rays [ID),[IE),[IF)[ID), [IE), [IF) at A′,B′,C′A',B',C'. Show that the orthocentre KK of △A′B′C′\vartriangle A'B'C' is on the line OIOI and that IKIO=rR\frac{IK}{IO}=\frac{r}{R}
Michel Bataille .
circumcircleincircleequal ratio