Secant-Tangent Theorem Worksheet

Secant-Tangent Theorem Worksheet

Read each question carefully and apply the Secant-Tangent Theorem to find the unknown values. Show all your work.

1. In your own words, explain the relationship between a tangent segment and a secant segment drawn from an external point to a circle, as described by the Secant-Tangent Theorem.

2. In the diagram below, a tangent segment and a secant segment are drawn to the circle from an external point. Find the length of x.

3. A tangent segment has a length of 12 units. The external part of a secant segment is 4 units. What is the length of the entire secant segment?

4. If a tangent segment from an external point to a circle is 8 units long, and the external part of a secant segment from the same point is 4 units long, what is the length of the internal part of the secant segment?

5. The Secant-Tangent Theorem states that if a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent segment is equal to the product of the length of the entire secant segment and its   part.

6. If the length of the tangent segment is 't', the length of the entire secant segment is 's', and the length of the external part of the secant segment is 'e', the theorem can be written as t² =  .

7. A tangent segment from point P to a circle has a length of 15 cm. A secant segment from point P intersects the circle at points A and B. If PA = 9 cm, find the length of AB.