MathDB
Collinearity [Switzerland 2011]

Source:

January 31, 2011
geometrycircumcirclegeometry proposed

Problem Statement

Let △ABC\triangle{ABC} a triangle with ∠CAB=90∘\angle{CAB}=90^{\circ} and LL a point on the segment BCBC. The circumcircle of triangle △ABL\triangle{ABL} intersects ACAC at MM and the circumcircle of triangle △CAL\triangle{CAL} intersects ABAB at NN. Show that LL, MM and NN are collinear.
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