SOLUTION: the segments GA and BG 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.

Algebra ->  -> SOLUTION: the segments GA and BG 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.       Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Mathway solves algebra homework problems with step-by-step help!

 Question 149128: the segments GA and BG 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 Edwin McCravy(9717)   (Show Source): You can put this solution on YOUR website!the segments GA and BG 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. ``` Label the center of the circle O. and draw radii to A and B. Let the radius be r Next draw OG which bisects the 48° angle G into two 24° angles. Let P be the point where OG intersects the circle. P is the nearest point on the circle to G, so GP is the distance we're looking for. Plan: Calculate the radius OA and the hypotenuse OG using the upper right triangle using trig ratios. Then calculate OG. Then since OP is also a radius, we will subtract the radius OP from OG and get GP. In the right triangle AOG, radius AO is the side opposite angle AGO which is 24°. GA is the side adjacent to angle AGO. So we use Put 1 under the Cross-multiply: Next we calculate OG: --- OG is the hypotenuse, GA is the opposite side of 24° So we use Put 1 under the Cross-multiply: So now we can find GP by subtraction, since OP = r = 12tan(24) GP = OG - OP = Edwin```