SOLUTION: The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.

Question 1158594: The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle. Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The segments GA and GB are tangent to a circle at A and B, and AGB is a 48-degree angle.
Given that GA = 12 cm, find the distance from G to the nearest point on the circle.
:
Draw a line from G, bisecting the 48 degree angle to the center of the circle
Draw the radius to points A and B
This forms two right triangles: one side = 12, one side = the radius and the
hypotenuse the line from G to the center.
the angles of this triangle, 24, 90 and 66 degrees
Use the tangent of 24 degrees to find the radius
tan(24) =
r = 5.343 is the radius
Find the hypotenuse (center to point g) using the cosine of 24 degrees
cos(24) =
h = 13.135
Find the distance from G to the circle
13.135 - 5.343 = 7.79 cm from G to the circle
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