# #20 of June 2017 Grade 10 CSAT (Korean SAT) mock test

Geometry Level 5

As shown above, there is a half circle whose diameter is segment $$\text{AB}$$ and radius is $$5$$.

Let $$\text{P}$$ be on the half circle.

A line segment that has midpoints of chord $$\text{AP}$$ and arc $$\text{AP}$$ as its ends is circle $$O_1$$'s diameter. Similarly, a line segment that has midpoints of chord $$\text{BP}$$ and arc $$\text{BP}$$ as its ends is circle $$O_2$$'s diameter.

Circle $$O$$ is an inscribed circle of $$\triangle\text{ABP}$$.

The minimum of the sum of the areas of $$O$$, $$O_1$$, and $$O_2$$ is $$S$$.

Find the value of $$\dfrac{144S}{\pi}$$.

This problem is a part of <Grade 10 CSAT Mock test> series.

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