Question

Two secant segments are drawn to a circle from a point outside the circle. The external segment of the first secant segment is 8 centimeters and its internal segment is 6 centimeters. If the entire length of the second secant segment is 28 centimeters, what is the length of its external segment?

Answer 1

Given:

Two secant segments are drawn to a circle from a point outside the circle.

External segment of the first secant segment = 8 centimeters

Internal segment of the first secant = 6 centimeters.

Entire length of the second secant segment = 28 centimeters.

To find:

The length of its external segment.

Solution:

Let x be the length of its external segment.

Entire length of the first secant segment = 8+6 = 14 centimeters.

If two secant segments are drawn to a circle from a point outside the circle, then product of entire length of first secant and external length of first secant is equal to product of entire length of second secant and external length of second secant.

$14\times 8=28\times x$

$112=28x$

Divide both sides by 28.

$\dfrac{112}{28}=x$

$4=x$

Therefore, the length of external segment of second secant is 4 centimeters.