Squared Distances on an Incircle

★ 7/10Circles AM-GM analytic geometry vectors

Problem

A moving line $l$ through the point $M(4,3)$ meets the positive $x$ -axis at a point $A$ and the positive $y$ -axis at a point $B$ . Among all such lines, take the one for which the area of $\triangle OAB$ is minimal, where $O$ is the origin. Let $P$ be a moving point on the incircle of that triangle $OAB$ . Find the range of

z=PO^2+PA^2+PB^2.

Answer

Solution

Difficulty	7/10
Topics	Circles, AM-GM, analytic geometry, vectors

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