Projections of Midpoints onto Circumradii
Projections of Midpoints onto Circumradii
Let ABC be an acute triangle with circumcenter O, circumradius , and inradius . Let A', B', and C' be the midpoints of BC, AC, and AB, respectively. Let D, D' be the projections of A' onto the circumradii OB and OC. Define E, E' and F, F' similarly for the points B' and C'. Then ++=.
R
r
DD'
BC
EE'
AC
FF'
AB
R+r
R