Given an acute triangle ABC. The incircle of triangle ABC touches BC,CA,AB respectively at D,E,F. The angle bisector of ∠A cuts DE and DF respectively at K and L. Suppose AA1 is one of the altitudes of triangle ABC, and M be the midpoint of BC.
(a) Prove that BK and CL are perpendicular with the angle bisector of ∠BAC.
(b) Show that A1KML is a cyclic quadrilateral. geometrytrigonometrycircumcircleangle bisectorperpendicular bisectorgeometry unsolved