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.
Central angle = Angle subtended by an arc of the circle from the center of the circle. Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle.
Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by
The following are short descriptions of the circle shown below.
Tangent - is a line that would pass through one point on the circle. Secant - is a line that would pass through two points on the circle. Chord - is a secant that would terminate on the circle itself. Diameter, d - is a chord that passes through the center of the circle. Radius, r - is one-half of the diameter.