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Circumcentre on circumcircle

Source: PRMO 2019 Leg 2 P9

August 25, 2019
geometryPRMOcircumcircle

Problem Statement

The centre of the circle passing through the midpoints of the sides of am isosceles triangle ABCABC lies on the circumcircle of triangle ABCABC. If the larger angle of triangle ABCABC is α∘\alpha^{\circ} and the smaller one β∘\beta^{\circ} then what is the value of α−β\alpha-\beta?
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