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|CA| |CD| = |AB| |AM| , angle bisectors, reflection of circumcenter related

Source: Dutch NMO 2019 p3

January 9, 2020
geometryangle bisectorreflectioncircumcircleCircumcenter

Problem Statement

Points A,BA, B, and CC lie on a circle with centre MM. The reflection of point MM in the line ABAB lies inside triangle ABCABC and is the intersection of the angle bisectors of angles AA and BB. Line AMAM intersects the circle again in point DD. Show that ∣CA∣⋅∣CD∣=∣AB∣⋅∣AM∣|CA| \cdot |CD| = |AB| \cdot |AM|.
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