A tangent line to circumcircle of acute triangle ABC (AC>AB) at A intersects with the extension of BC at P. O is the circumcenter of triangle ABC.Point X lying on OP such that ∡AXP=90∘.Points E and F lying on AB and AC,respectively,and they are in one side of line OP such that ∡EXP=∡ACX and ∡FXO=∡ABX.
K,L are points of intersection EF with circumcircle of triangle ABC.prove that OP is tangent to circumcircle of triangle KLX.Author:Mehdi E'tesami Fard , Iran geometrycircumcirclereflectionIran