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OB=OC wanted, 2 circumcircles, 1 midpoint, orthocenter

Source: Mathematics Regional Olympiad of Mexico West 2020 P6

September 9, 2022
geometryequal segments

Problem Statement

Let M M be the midpoint of side BC BC of a scalene triangle ABC ABC . The circle passing through A A , B B and M M intersects side AC AC again at D D . The circle passing through A A , C C and M M cuts side AB AB again at E E . Let O O be the circumcenter of triangle ADE ADE . Prove that OB=OC OB=OC .
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