Jonah and Candice were two long distance lovers. Jonah
lived in Chicago, and Candice lived in New York.

Jonah was eager to get married soon. Candice, who wanted to concentrate on her career, wanted to delay for at least two years.

Knowing that Chicago and New York have a time difference of an hour, Candice told Jonah over the phone that if he proposed at a time when both Chicago and New York have the same time, she would agree to get married right away.

Within a month, Jonah proposed, and Candice agreed. And the married couple, at least for Jonah, lived happily ever after.

How did this happen? When did Jonah propose?

Given a circle and two points on that circle,

*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*.