MathDB
Just angles

Source: 2019 Belarus Team Selection Test 7.1

September 2, 2019
geometry

Problem Statement

The internal bisectors of angles ∠DAB\angle DAB and ∠BCD\angle BCD of a quadrilateral ABCDABCD intersect at the point X1X_1, and the external bisectors of these angles intersect at the point X2X_2. The internal bisectors of angles ∠ABC\angle ABC and ∠CDA\angle CDA intersect at the point Y1Y_1, and the external bisectors of these angles intersect at the point Y2Y_2. Prove that the angle between the lines X1X2X_1X_2 and Y1Y2Y_1Y_2 equals the angle between the diagonals ACAC and BDBD.
(A. Voidelevich)
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