MathDB

6.1

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 6.1 sum of \delta_(I_x)=4R

Source:

6/7/2020
Show that the circumradius RR of a triangle ABCABC equals the arithmetic mean of the oriented distances from its incenter II and three excenters Ia,Ib,IcI_a,I_b, I_c to any tangent τ\tau to its circumcircle. In other words, if δ(P)\delta(P) denotes the distance from a point PP to τ\tau, then with appropriate choices of signs, we have δ(I)±δ(Ia)±δ(Ib)±δ(Ic)=4R\delta(I) \pm \delta_(I_a) \pm \delta_(I_b) \pm \delta_(I_c) = 4R Luis González
geometrycircumradiusexcenterincenterdistancecircumcircleTangents