# Circumspection

M is any point on the line AB. Squares of side length AM and MB are
constructed and their circumcircles intersect at P (and M). Prove
that the lines AD and BE produced pass through P.

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M).

Prove that the lines AD and BE produced pass through P.

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Look for angles which will help you to show that the angles in question are $180^{\circ}$ so the lines are straight.

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M).

Pick up a pencil, do some drawing, play with this. Look at angles APM, MPD, AEM, MCD and look for cyclic quadrilaterals. The proof that the lines AD and BE produced pass through P takes three or four lines.