Minimizing a Segment with a Right-Angle Constraint

★ 6/10plane geometry Extrema Tangent Circle

Problem

As shown, $\angle B=\angle CDE=90^{\circ}$ , $BC=6$ , and $AB=8$ . Point $D$ lies on segment $AB$ , and point $E$ lies on segment $CA$ . Find the value of $BD$ for which $CE$ is shortest, and find the minimum value of $CE$ .

Answer

Solution

Difficulty	6/10
Topics	plane geometry, Extrema, Tangent Circle

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