Question

A tangent segment and a secant segment are drawn to a circle from a point outside the circle. the length of the tangent segment is 15 inches. the external segment of the secant segment measures 5 inches. what is the measure of the internal secant segment? type in the number only for the answer.

Answer 1

Using the Power of a Point Theorem, the internal segment of the secant is calculated to be 40 inches, given the lengths of the tangent segment (15 inches) and the external secant segment (5 inches).

Step-by-step explanation:

The student is asking about the properties of tangent and secant lines to a circle, which involves finding the length of the internal segment of the secant when given the external segment and the length of a tangent from the same point.

According to the Power of a Point Theorem (also known as the Tangent-Secant Theorem), the square of the length of the tangent segment (tangent from the external point to the point of tangency) is equal to the product of the lengths of the external segment and the whole secant (external plus internal segment) of the secant line.

Given that the tangent segment is 15 inches and the external segment of the secant is 5 inches, we set up the equation: 15^2 = 5 × (5 + internal segment).

Solving for the internal segment, we get internal segment = (15^2 / 5) - 5.

After calculation, the internal segment of the secant measures 40 inches.