A Trapezoid Coefficient Minimum

★ 8/10plane geometry Parametrization Circles Trigonometric Identities vectors

Problem

In a trapezoid $ABCD$ , $\overrightarrow{BC}=2\overrightarrow{AD}$ and $AB=AD=CD$ . A point $P$ in the plane satisfies $\overrightarrow{PB}\cdot\overrightarrow{PC}=0$ and

\overrightarrow{PB}=x\overrightarrow{PA}+y\overrightarrow{PC},

where $x>0$ and $y>0$ . Find the minimum value of $x+y$ .

Answer

Solution

Difficulty	8/10
Topics	plane geometry, Parametrization, Circles, Trigonometric Identities, vectors

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