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. : 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(2087) (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
