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 the diagram below, a tangent segment and a secant segment are drawn to a circle from an exterior point. If the tangent segment measures 8 units and the external segment of the secant measures 4 units, what is the length of the entire secant segment?

2. A tangent segment from an external point to a circle is 12 cm long. The secant segment from the same external point has an external part of 6 cm. Find the length of the internal part of the secant segment.

3. The Secant-Tangent Theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior 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.

4. If a tangent segment has a length of 't' and a secant segment has an external part 'e' and an internal part 'i', the theorem can be expressed as t² = e * ( ).

5. The Secant-Tangent Theorem can be used to find the length of a tangent segment if the lengths of the external and internal parts of a secant segment are known.

6. The Secant-Tangent Theorem is only applicable when the tangent and secant segments intersect outside the circle.

7. In a circle, a tangent segment has a length of 6 units. A secant segment from the same exterior point has an external part of 3 units. What is the length of the entire secant segment?

8. If a tangent segment is 10 units long and the entire secant segment is 25 units long, what is the length of the external part of the secant segment?