# In honour of I.F.Sharygin.

Geometry Level 4

Let $$O$$ and $$H$$ be the circumcenter and the orthocenter of a $$\triangle ABC$$ respectively. The line passing through the midpoint of $$OH$$ and parallel to $$BC$$ meets $$AB$$ and $$AC$$ at points $$D$$ and $$E$$ respectively. It is known that $$O$$ is the incenter of $$\triangle ADE$$. Find the measure of $$\angle A$$ in degree measures.

Source:- SGO Class 8..

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