# Day 10: Astonishing Geometry

Geometry Level 5

In a triangle $$ABC$$, a circle centred at $$O$$, passing through $$B$$ and $$C$$, is drawn such that $$\angle BOC = 144^{\circ}$$ where $$O$$ is on the side of $$BC$$ not containing $$A$$. The circle intersects $$AB$$ and $$AC$$ again at $$P$$ and $$Q$$ respectively. It is given that the incentre $$I$$ of $$APQ$$ lies on the circle.

Find $$\angle BAO$$.

This problem is part of the set Advent Calendar 2014.

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