Theorems

Theorem 7 - The Tangent-Secant Theorem

• Given an angle with its vertex on the circle, formed by a secant ray and a tangent ray, the measure of the angle is one-half the measure of the intercepted arc.

Theorem 8

• If two chords intersect within a circle, then the measure of the angle formed is equal to one-half the sum of the measures of the intercepted arcs.

Theorem 9

• If a tangent and a secant, two secants, or two tangents intersect in a point in the exterior of a circle, then the measure of the angle formed is equal to one-half the difference of the measures of the intercepted arcs.

Theorem 10

• If two chords intersect inside a circle, then the product of the lengths of the segment parts of one chord is equal to the product of the lengths of the segment parts of the other chord.

Theorem 11

• If two secants intersect in the exterior of a circle, then the product of the lengths of one secant and its external segment part is equal to the product of the lengths of the other segment and its external segment.

Theorem 12

• If a secant and a tangent intersect in the exterior of a circle, then the product of the lengths of the secant segment and its external segment part is equal to the square of the length of the tangent segment.