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# Geometry

Let $$ABC$$ be a right-angled triangle with $$\angle B= 90^\circ$$. Let $$BD$$ be the altitude from $$B$$ on to $$AC$$. Let $$P, Q$$ and $$I$$ be the incenters of triangles $$ABD, CBD$$ and $$ABC$$, respectively. Show that the circumcentre of the triangle $$PIQ$$ lies on the hypothenuse $$AC$$.

Note by Saikat Sengupta
1 month, 4 weeks ago

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