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Another geometry

Source: St Petersburg Olympiad 2014, Grade 11, P4

October 24, 2017
geometrycircumcircle

Problem Statement

Points B1,C1B_1,C_1 are on ACAC and ABAB and B1C1∥BCB_1C_1 \parallel BC. Circumcircle of ABB1ABB_1 intersect CC1CC_1 at LL. Circumcircle CLB1CLB_1 is tangent to ALAL. Prove AL≤AC+AC12AL \leq \frac{AC+AC_1}{2}
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