how long is the tangent segment AC?

Question

Given circle B , line AC is tangent to the circle. Sally connects the point of tangency A to the center of circle B. She also draws a segment BC and it has a length of 10 cm. If the radius of the circle is 6 cm, how long is the tangent segment AC?

Answer 1

draw a diagram

the radius, the tangent, and the segment BC form a right triangle with BC being the hypotenuse

it is a right triangle because the radius, AB, is perpendicular to the tangent, AC, at the point of tangency

any radius is perpendicular to a tangent at the point of tangency

use the Pythagorean Theorem

10²=6²+x² where x is the length of the tangent

100=36+x²

100-36=x²

x²=64

x=√64

x=8 cm

this is an example of a 3-4-5 right triangle (2*3, 2*4, 2*5)