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BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC.If L is the mid-point of BC,prove that LM=LN



Well, it is an easy problem.what u have to do is just complete the trapezium BMCN. now BM || CN. then u construct a perpendicular from L to the line and extend it such that it intersects BN at X, CM at Y and MN at K. now applying midpoint theorem to the triangles BCM and BCN ( using the fact that XY || BM || CN and L is the midpoint of BC, you can easily prove that K is the midpoint of MN. now in triangle LMN, LK is perpendicular to MN and bisects it which is possible only when the triangle is isoceles. therefore LM=LN.
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