**EMAT
6700**

**by
Brad Simmons**

**Constructing a Decagon**

Use geometer's sketchpad to construct a decagon.

1. Construct circle O of radius 1 unit, tangent to a line at point A.

2. Mark off 2 unit from point A to locate point P on the line.

3. Construct segment OP and label point Q where the segment intersects the circle.

(By the Pythagorean Theorem, segment OP = the square root of 5. Segment PQ = (the square root of 5) minus 1.)

4. Bisect segment PQ and label the midpoint as R.

(The segment PR has a length ((the square root of 5) minus 1) divided by 2.)

5. Select segment PR and point A. Construct circle by center and radius.

6. Use a radius of the length of segment PR to mark 10 points around the circle.

7. Connect the 10 point to form a decagon.

8. Hide the construction objects.

Please click here for a geometer's sketchpad sketch of the figure shown above.

**What
is the measure of angle AOB?**

**What
is the measure of segment AB?**

**What
is the measure of segment AB if left in radical form?**

Please click here for a geometer's sketchpad sketch of the figure shown above.