### First Method. When The Sides Intersect

Draw the lines O C and O A - about 3 inches long - forming any angle of 45 to 60 degrees. With 0 as a center and any convenient radius - about 2 inches - draw an arc intersecting the sides of the angle at E and F. With E and F as centers and a radius of 1 1/2 or 1 3/4 inches, describe short arcs intersecting at I. A line O D, drawn through the points 0 and /, bisects the angle.

In solving this problem the arc E F should not be too near the vertex if accuracy is desired.

### Proof

The central angles A O D and D O C are equal because the arc E F is bisected by the line O D. The point I is equally distant from E and F.

### Second Method. When The Lines Do Not Intersect

Draw the lines A C and E F about 4 inches long making an angle approximately as shown. Draw A' C' and E' F' parallel to A C and E F and at such equal distances from them that they will intersect at O. Now bisect the angle C' O F' by the method given in Problem 8. The line O R bisects the given angle.

### Proof

Since A' C is parallel to A C and E' F' is parallel to E F, the angle C' O F' is equal to the angle formed by the lines A C and E F. Hence as O R bisects angle C' O F' it also bisects the angle formed by the lines A C and E F.