The Brocard Point of a Right Triangle

★ 6/10Tangent Circle Circles AM-GM analytic geometry

Problem

Let $a > 0$ , $A(2a, 0)$ , $B(0, 2)$ , and let $O$ be the origin.

1. Find the standard equation of the circle that has $OA$ as a chord and is tangent to line $AB$ at $A$ . 2. This circle meets the circle with diameter $OB$ at a point $P$ in the first quadrant (called the Brocard point of right triangle $OAB$ ). Find the maximum possible $x$ -coordinate of $P$ .

Answer

Solution

Difficulty	6/10
Topics	Tangent Circle, Circles, AM-GM, analytic geometry

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