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MathNet 2026 — Part 01 Question 185

Math Olympiad Vault · MathNet 2026 — Part 01

Question 185

The following figure shows a segment $AB$, its midpoint $C$ and the semi-circumferences of diameters $AB$ e $AC$. a center circle $P$ It is tangent to the two semi-circumferences and also to the segment $AB$. being $AB=8~\mathrm{cm}$, e $O$, the midpoint of $AC$, ask yourself:
Question illustration


a) what is the perimeter of the triangle $OCP$?


b) What is the radius of the center circle $P$?