# Homework Help: Inscribing a quadrilateral in a circle

1. Aug 1, 2007

### ehrenfest

1. The problem statement, all variables and given/known data

If both pairs of opposite angles of a quadrilateral add up to 180, is it always possible to inscribe it in a circle?

2. Relevant equations

3. The attempt at a solution

The converse is easily proven, since the angle between two chords standing on the circumfrence is half of the corresponding central angle.

2. Aug 1, 2007

### chaoseverlasting

If by inscribe, you mean that all four vertices lie on the circle, I dont think so.

3. Aug 1, 2007

### Dick

It is true. Draw the circle containing three points of the quadrilateral and then use the supplementary angle property to show the fourth point must lie on the circle.

4. Aug 1, 2007

### chaoseverlasting

Yes, but if only two points lie on the circle, then the other two dont necessarily have to. Thats what I was thinking about. The same obviously goes for one point lying on the circle.

In any case, the opposite angles of a quadrilateral will always be supplementary.

5. Aug 1, 2007

### ehrenfest

No, e.g. a diamond.

6. Aug 1, 2007

### Dick

You can put a circle through any three noncollinear points.