# Ridiculous length!

Level pending

In acute $$\triangle ABC$$,$$AB<AC$$ and $$\angle A = 60^{\circ}$$ , $$H$$ is the orthocentre, $$I$$ is the incentre and $$D$$ is the midpoint of $$BC$$. The line passing through $$D$$ and $$I$$ intersects the straight line through $$A$$ parallel to $$BC$$ at $$P$$. Suppose $$\sin \angle B - \sin \angle C = \dfrac{3}{5}$$ and $$AH = 10$$ .What is the numerical value of $$AP$$ ?

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