MathDB
independent of the position of D

Source: 3rd JBMO 1999

June 16, 2004
geometrycircumcircletrigonometryperpendicular bisectorJBMO

Problem Statement

Let ABCABC be a triangle with AB=ACAB=AC. Also, let D∈[BC]D\in[BC] be a point such that BC>BD>DC>0BC>BD>DC>0, and let C1,C2\mathcal{C}_1,\mathcal{C}_2 be the circumcircles of the triangles ABDABD and ADCADC respectively. Let BB′BB' and CC′CC' be diameters in the two circles, and let MM be the midpoint of B′C′B'C'. Prove that the area of the triangle MBCMBC is constant (i.e. it does not depend on the choice of the point DD). Greece
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