Problem 247, FJGC
Let O be the circumcenter of triangle ABC and A' reflection of A about BO. AA' intersects BC at U. Prove that C and U are inverses of each other w.r.t. circle (B,BA)
Proof:
BC is angle bisector of <ACA', thus <A'CB=<ACB=<BAA', so AB is tangent to the circle (AUC), giving AB.AB=BU.BC, done.
Niciun comentariu:
Trimiteți un comentariu