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triangle construction by 4 points,C,L of bisector + M,N touchpoints of incircle

Source: 2012 Sharygin Geometry Olympiad Final Round 9.3

August 3, 2018
geometryangle bisectorconstruction

Problem Statement

In triangle ABCABC, the bisector CLCL was drawn. The incircles of triangles CALCAL and CBLCBL touch ABAB at points MM and NN respectively. Points MM and NN are marked on the picture, and then the whole picture except the points A,L,MA, L, M, and NN is erased. Restore the triangle using a compass and a ruler.
(V.Protasov)
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