Question

Consider a cicle with AB as diameter and P another point on the circle. Let M...

Consider a cicle with AB as diameter and P another point on the circle. Let M be the foot of the perpendicular from P to AB. Draw the circles which have AM and M B respectively as diameters, which meet AP at Q are BP are R. Prove that QR is tangent to both circles.

Hint: As well as the line QR, draw in the line segments M Q and M R.

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