A Max of a Perimeter Defect

★ 7/10plane geometry Extrema Tangent Circle analytic geometry

Problem

In the first quadrant of the coordinate plane $xOy$ , a point $P$ satisfies $OP=1$ and the line $OP$ has inclination $30^\circ$ . An arbitrary line through $P$ meets the positive $x$ -axis at $M$ and the positive $y$ -axis at $N$ . Find the maximum value of $OM+ON-MN$ .

Answer

Solution

Difficulty	7/10
Topics	plane geometry, Extrema, Tangent Circle, analytic geometry

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