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Relating the circumdiameter to a triangle in the incircle

Source: Canada Repêchage 2021/4 CMOQR

March 30, 2021
Canadarepechagegeometryincirclecircumcircle

Problem Statement

Let OO be the centre of the circumcircle of triangle ABCABC and let II be the centre of the incircle of triangle ABCABC. A line passing through the point II is perpendicular to the line IOIO and passes through the incircle at points PP and QQ. Prove that the diameter of the circumcircle is equal to the perimeter of triangle OPQOPQ.
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