Problem A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

Answer Key

Solution

$r(\pi - \theta) = 2640$

$r = \dfrac{2640}{\pi - \theta}$

$r = \dfrac{2640}{\pi - \arctan \left( \dfrac{5280}{r} \right)}$

$r = 1437.44 ~ \text{ft.}$ ← answer

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