To draw a Tangent to a circle.
—I. Let B ([Fig. 11]) be the point from which it is required to draw the tangent. Draw the radius O B, and at B erect a perpendicular (see [Fig. 2]); then will the line B D be a tangent to the circle. II. It is required to draw a tangent from the point E in the same circle. Draw the radius O E extending beyond the circumference to F, and make E G equal to E F. From F and G, with any radius, describe arcs cutting each other in H and I; then a line drawn through these points will be a tangent to the circumference at E.
Fig. 12.
To find the Centre of a circle.
—From any point in the circumference, as B, ([Fig. 12]), describe an arc cutting the circumference in A and C, and from A and C, with the same radius, describe arcs cutting the first arc in two points; through the points of intersection draw lines to the interior of the circle, and the point O where these lines intersect will be the centre of the circle.
Fig. 13.
