Question 1115257
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It seems there should be an easier way... but here is one.<br>
(You will need to draw this out to follow the proof.)<br>
Let the centers of the circles be C and D, with AC a radius of one of the circles and BD a radius of the other.
Let PE be a diameter of the circle with center C; let PF be a diameter of the other circle.<br>
AC is parallel to BD; so arcs AE and BP have the same measure, as do arcs AP and BF.<br>
Furthermore, the sum of the measures of arcs AE and BF is 180 degrees, because EP and PF are diameters of the two circles.<br>
The measure of angle EPA is half the measure of arc AE; the measure of angle FPB is half the measure of arc BF.  Since the sum of the measures of those two arcs is 180 degrees, the sum of the measures of angles EPA and FPB is 90 degrees.<br>
But that makes the measure of angle BPA 90 degrees.