Is there a formula for calculating the point equidistant from the start point and end point of an arc given:

1) An arc is defined as: A center point $P$, a radius $r$ from the center, a starting angle $sA$ and an ending angle $eA$ in $radians$ where the arc is defined from the starting angle to the ending angle in a counter-clockwise direction.

2) The start point $sP$ is calculated as: $sP\{Px + \cos sA \times r, Py + -\sin sA \times r\}$

3) The end point $eP$ is calculated as: $eP\{Px + \cos eA \times r, Py + -\sin eA \times r\}$

Give the above restrictions, is there a way to calculate the point that is halfway between the start and end angles and exactly $r$ units away from the center?