MathDB

14

Part of 2013 Sharygin Geometry Olympiad

Problems(1)

Right-angled trapezoid ABCD

Source: Sharygin First Round 2013, Problem 14

4/4/2013
Let MM, NN be the midpoints of diagonals ACAC, BDBD of a right-angled trapezoid ABCDABCD (∡A=∡D=90∘\measuredangle A=\measuredangle D = 90^\circ). The circumcircles of triangles ABNABN, CDMCDM meet the line BCBC in the points QQ, RR. Prove that the distances from QQ, RR to the midpoint of MNMN are equal.
geometrytrapezoidcircumcircleanalytic geometryquadraticsAsymptotetrigonometry