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SMO 2010 Junior Round 1 Question 29

SMO · SMO 2010 Junior Round 1

Question 29

Let $ABCD$ be a rectangle with $AB=10$. Draw circles $C_1,C_2$ with diameters $AB,CD$ respectively. Let $P,Q$ be their intersection points. If the circle with diameter $PQ$ is tangent to $AB$ and $CD$, what is the area of the shaded region?

Question illustration