SOLUTION: The segments GA and GB are tangent to a circle at A and B, and AGB is a 60-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The segments GA and GB are tangent to a circle at A and B, and AGB is a 60-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1158588: The segments GA and GB are tangent to a circle at A and B, and AGB is a 60-degree
angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Let C be the center of the circle; let P be the point of intersection of CG and the circle.

The shortest distance from G to a point on the circle is the length of GP.

Angle AGB is 60 degrees, so angle AGC is 30 degrees.

Then triangle AGC is a 30-60-90 right triangle.

AG=12 means AC=6 and CG=6*sqrt(3).

CP is also 6; that makes GP 6*sqrt(3)-6.

ANSWER: 6*sqrt(3)-6