MathDB
JBMO Shortlist 2020 G1

Source: JBMO Shortlist 2020

July 4, 2021
JuniorBalkanshortlist2020geometry

Problem Statement

Let △ABC\triangle ABC be an acute triangle. The line through AA perpendicular to BCBC intersects BCBC at DD. Let EE be the midpoint of ADAD and ω\omega the the circle with center EE and radius equal to AEAE. The line BEBE intersects ω\omega at a point XX such that XX and BB are not on the same side of ADAD and the line CECE intersects ω\omega at a point YY such that CC and YY are not on the same side of ADAD. If both of the intersection points of the circumcircles of △BDX\triangle BDX and △CDY\triangle CDY lie on the line ADAD, prove that AB=ACAB = AC.
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