An Isosceles Vertex Locus

★ 7/10plane geometry Circles analytic geometry Triangle Geometry

Problem

In the coordinate plane, $B$ moves along the curve $y = \sqrt{1 - x^2}$ , and $A(2, 0)$ . A point $C$ in the first quadrant makes $\triangle ABC$ an isosceles right triangle with the right angle at $A$ . Find the maximum possible length of segment $OC$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Circles, analytic geometry, Triangle Geometry

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