A line that is tangent to a circle at a given point is perpendicular to the radius that intersects the point. It follows that one method of drawing a line tangent to a circle at a given point is to draw the radius that intersects the point, and then draw the line tangent at the point of intersection and perpendicular to the radius.

Another method is shown in figure 4-32. To draw a line tangent to the circle at P, set a compass to the radius of the circle, and, with P as a center, strike an arc that intersects the circle at A. With the compass still set to the radius of the circle, use A as a center and strike an arc that intersects the first arc at B. With B as a center and the compass still set to the radius of the circle, strike another arc. A line through the point of intersection (0) of the last drawn arc and through P is tangent to the circle at P.

CIRCULAR ARC OF A GIVEN RADIUS TANGENT TO TWO STRAIGHT LINES

Drawing a fillet or round comprises the problem of drawing a circular arc of a given radius tangent to two nonparallel lines.

Figure 4-33 shows a method that can be used when the two nonparallel lines form a right angle. AB is the given radius of the arc. Set a compass to this radius, and, with the point of intersection of the lines as a center, strike an arc intersecting the lines at C and D. With C and D as centers and the same radius, strike intersecting arcs as

Figure 4-33.-Circular arc tangent to two lines that form a right angle.

shown. The point of intersection of these arcs (0) is the center of the circle of which an arc of the given radius is tangent to the lines.

Figure 4-34 shows a method that can be used regardless of the size of the angle formed by the lines. Again AB equals the given radius of the arc, and the problem is to draw an arc with radius equal to AB, tangent to CD and EF. Draw GH parallel to CD and at a distance from CD equal to the given radius of the arc. Draw IJ parallel to EF and also at a distance equal to the given radius of the arc. The point of intersection between GH and IJ (P) is the center of the circle of which an arc of the given radius is tangent to CD and EF.