document.write( "Question 1167004: Consider Triangle ABC. A circle k passes through points A and B and intersects CA and CB in points N and M, repectively. Prove that Triangle ABC is similar to Triangle MNC \n" ); document.write( "

Algebra.Com's Answer #791631 by math_helper(2461) $\"\"$ $\"About$

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document.write( "By the secant theorem:
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document.write( "|AC|*|CN| = |BC|*|CM|     (note that CM and CN are the sections outside the circle)\r
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document.write( "Now notice |AC|/|CM| = c = |BC|/|CN|   which means we have two sides of two triangles with a common ratio of side lengths (here, AC corresponds to CM and BC corresponds to CN).   Note also that angle ACB is common to both triangles and is the included angle, thus by SAS triangles ABC and NMC are similar. \r
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