Secant-Tangent Theorem Worksheet

Secant-Tangent Theorem Worksheet

Read each question carefully and solve for the unknown angles or lengths. Show all your work for full credit.

1. In the diagram below, a tangent segment and a secant segment are drawn to a circle from an external point. If the measure of the intercepted arc closest to the external point is 70° and the measure of the intercepted arc farthest from the external point is 190°, what is the measure of the angle formed by the tangent and secant?

2. According to the Secant-Tangent Theorem, the measure of an angle formed by a tangent and a secant drawn from an external point to a circle is half the   of the measures of the intercepted arcs.

3. If a tangent segment and a secant segment meet at an external point P, and the major arc intercepted is 240° and the minor arc intercepted is 80°, then the angle formed at P is   degrees.

4. A tangent segment and a secant segment are drawn to a circle from an external point. The measures of the intercepted arcs are 150° and 50°. What is the measure of the angle formed by the tangent and secant?

5. A point P lies outside a circle. A tangent segment PA and a secant segment PBC are drawn from P to the circle, where A, B, and C are points on the circle. If the measure of arc AC is 180° and the measure of arc AB is 60°, find the measure of angle APC.

6. The Secant-Tangent Theorem can be used when the tangent and secant intersect inside the circle.