A Folded Triangle Minimum

Problem

In a right triangle $ABC$ with the right angle at $B$ , $AB=1$ and $BC=2$ . A point $D$ moves along the hypotenuse $AC$ . The triangle $ABD$ is folded along $BD$ to a triangle $A_1BD$ so that the dihedral angle $A\text{-}BD\text{-}A_1$ equals $\dfrac{\pi}3$ . Find the minimum value of $A_1C$ .

Answer

Solution

Difficulty	8/10
Topics	Extrema, solid geometry, Circles

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