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Prove that AW=WT

Source: MEMO 2018 T6

September 3, 2018
geometrycircumcircleMEMO 2018

Problem Statement

Let ABCABC be a triangle . The internal bisector of ABCABC intersects the side ACAC at L L and the circumcircle of ABCABC again at W≠B.W \neq B. Let KK be the perpendicular projection of LL onto AW.AW. the circumcircle of BLCBLC intersects line CKCK again at P≠C.P \neq C. Lines BPBP and AWAW meet at point T.T. Prove that AW=WT.AW=WT.
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