A secant and tangent are drawn to a circle from a common exterior point if the length of the tangent is 14 inches and the length of the external segment of the secant is 4 inches then what is the length of the internal segment of the secant

  45 inches

Step-by-step explanation:

The product of distances from a point to the two intersections of the secant with the circle is a constant. When the secant is a tangent, the two intersection points have the same distance, so the constant is the square of the tangent length.

Here, we have ...

  CD² = CB·CA

  14² = 4(4 +BA)

  49 = 4 +BA . . . . . . divide by 4

  45 = BA . . . . . . . . . subtract 4

The length of the internal segment of the secant is 45 inches.

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step-by-step explanation: