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2018 preRMO p8, angle chasing with a chord

Source:

August 8, 2019
anglesgeometrychord

Problem Statement

Let ABAB be a chord of a circle with centre OO. Let CC be a point on the circle such that ∠ABC=30o\angle ABC =30^o and OO lies inside the triangle ABCABC. Let DD be a point on ABAB such that ∠DCO=∠OCB=20o\angle DCO = \angle OCB = 20^o. Find the measure of ∠CDO\angle CDO in degrees.
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