Asked by logi
Two circles have a radii of 15 and 95. If the two external tangents to the circles intersect at 60 degrees, how far apart are the centers of the circles?
Can someone please explain this to me, show the work and give me the answer. Thanks!
Can someone please explain this to me, show the work and give me the answer. Thanks!
Answers
Answered by
Steve
As usual, draw a diagram. If the smaller circle has center O and the larger circle has center P, and the tangent on one side touches O at A and P at B, then draw AC parallel to OP, intersecting PB at Q.
Note that AQ = OP and you have a right triangle AQB where
angle QAB = 30°
QB = 80
So, the distance between the centers, OP = AQ = 80√3
Note that AQ = OP and you have a right triangle AQB where
angle QAB = 30°
QB = 80
So, the distance between the centers, OP = AQ = 80√3
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