In a triangle ABC (figure below), O
is the circumcircle, AD, BE, and CF are bisectors of angle A, B,
and C (D,E,F on circle O). G is a point on AB. GH is parallel to
AD so that angle HBE = 90 degrees. GJ is parallel to BE so that
angle JAD = 90 degrees. Prove that (1)
Lines JE, FG, and HD are concurrent at a point K; (2) K lies on
circle O.
See
also:
Triangle
Circle
Circumcircle
Angle Bisector
90 degrees
Parallel lines
Concurrent lines
