MathDB
11st ibmo - costa rica 1996/q2.

Source: Spanish Communities

April 23, 2006
geometrycircumcircle

Problem Statement

Let △ABC\triangle{ABC} be a triangle, DD the midpoint of BCBC, and MM be the midpoint of ADAD. The line BMBM intersects the side ACAC on the point NN. Show that ABAB is tangent to the circuncircle to the triangle △NBC\triangle{NBC} if and only if the following equality is true: BMMN=(BC)2(BN)2.\frac{{BM}}{{MN}} =\frac{({BC})^2}{({BN})^2}.
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