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OMK 2018 Sulong, Section A Problem 4

Source: OMK 2018 Sulong, Section A Problem 4

June 21, 2021
geometrycontests

Problem Statement

Given a circle with diameter ABAB. Points CC and DD are selected on the circumference of the circle such that the chord CDCD intersects ABAB inside the circle, at point PP. The ratio of the arc length \overarc {AC} to the arc length \overarc {BD} is 4:14 : 1 , while the ratio of the arc length \overarc{AD} to the arc length \overarc {BC} is 3:23 : 2 . Find ∠APC\angle{APC} , in degrees.
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