Problem
Let ABC be the triangle with AB = 1, AC = 3, and ∠BAC = π/2. If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle ABC, then find the value of r.
Solution
Comments
A simple problem based on applying coordinate or analytical geometry to a pure geometry situation.
A similar problem for you: What’s the value of r if the circle (of radius r) touches the circumcircle externally? Something to note: In this case, the circle will touch the sides of the triangle when they’re extended.