SOLUTION: The centers of 2 coplanar circles of radii 4 and 11 are 25 apart. Find the length of a segment that is a common internal tangent segment of the 2 circles.
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-> SOLUTION: The centers of 2 coplanar circles of radii 4 and 11 are 25 apart. Find the length of a segment that is a common internal tangent segment of the 2 circles.
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Question 1147051: The centers of 2 coplanar circles of radii 4 and 11 are 25 apart. Find the length of a segment that is a common internal tangent segment of the 2 circles. Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
I'll describe the method of solution and let you do the work....
(1) Draw the two circles and the common internal tangent.
(2) Draw the radii of the two circles to the points of tangency. Note that those radii are perpendicular to the tangent.
(3) Form a rectangle using the common internal tangent and one of those radii as the length and width.
(4) The diagram will now have a right triangle with the line joining the centers of the two circles as the hypotenuse and a line segment with a length equal to the length of the tangent as one leg.
(5) Use the Pythagorean Theorem to determine the length of the tangent.
Comment added after seeing the response from tutor @ikleyn....
The solution method shown in the place referenced in her response is a perfectly valid method. A good student should be able to understand it, as it uses many useful mathematical ideas.
Note, however, that it requires FAR more work than the method described in my response....
