The two circles shown are internally tangent at point A. The center of the larger circle is B, while the center of the smaller circle is G. The length of line segment CD is 90 mm, while the length of line segment EF is 50 mm. Line AD is perpendicular to line FB. Determine the length of the diameter of each circle.
E being on the small circle diameter [AC]
AEC is a right-angle triangle
AE² + EC² = AC²
Now express each of the three lengths in terms of R (radius of the big circle), r (radius of the small circle), CD and EF
You will find an equation from which you can find R and then r
Jul 15th 2010, 08:27 PM
"Now express each of the three lengths in terms of R (radius of the big circle), r (radius of the small circle), CD and EF"
I cannot figure out what you mean by this
Jul 16th 2010, 06:42 AM
Jul 17th 2010, 02:02 PM
I got it! Thank you so much
Jul 18th 2010, 10:57 AM
There is an easy solution to this if you know that the altitude to the hypotenuse of a right triangle is the geometric mean of the hypotenuse segments. Try it as a check for your answers.