Drag the external point P around outside a circle. Two tangent lines run from P to touch the circle at A and B. The blue wedge at P is the angle between the two tangents; the gold wedge at the center O is the central angle of the arc between the touch points. The two angles always add to 180 degrees, and the tangent angle equals half the difference between the far arc and the near arc. The two tangent segments PA and PB are always equal, and each radius meets its tangent at a right angle. A rim handle resizes the circle. An info button opens a drawer explaining the theorem.