*P*and

*Q*, draw the chord

*PQ*, and label its midpoint

*M*.

Now draw two other chords of the circle *AB* and *CD* that both pass through *M*.

Further, draw chords *AD* and *BC*.

Label the intersection of *AD* and *PQ*, point *X*.

Label the intersection of *BC* and *PQ*, point *Y*.

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Prove that *M* is the midpoint of line segment *XY*.