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Containment in a circle

Source: Brazil National Olympiad 2019 - level 2 - #4

November 23, 2019
euclidean geometrygeometryBrazilian Math Olympiad

Problem Statement

Let ABC ABC be an acutangle triangle and D D any point on the BC BC side. Let E E be the symmetrical of D D in AC AC and F F is the symmetrical D D relative to AB AB . A A straight ED ED intersects straight AB AB at G G , while straight FD F D intersects the line AC AC in H H . Prove that the points A,E,F,G A, E, F, G and H H are on the same circumference.
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