Let-denote-the-circumcircle-of-ABC-The-tangent-to-at-A-meets-BC-at-X-Let-the-angle-bisectors-of-AXB-meet-AC-and-AB-at-E-and-F-respectively-D-is-the-foot-of-the-angle-bisector-from-BAC-on-BC-

Question Number 112199 by Aina Samuel Temidayo last updated on 06/Sep/20

Let Ω denote the circumcircle of ABC .

The tangent to Ω at A meets BC at X .

Let the angle bisectors of ∠ AXB meet

AC and AB at E and F

respectively . D is the foot of the angle

bisector from ∠ BAC on BC . Let AD

intersect EF at K and Ω again at

L (other than A) . Prove that AEDF is

a rhombus and further prove that the

circle defined by triangle KLX passes

through the midpoint of line segment

BC .