# Finding Circle Diameter

• Jul 15th 2010, 10:16 AM
MATNTRNG
Finding Circle Diameter
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.

Attachment 18206
• Jul 15th 2010, 10:57 AM
running-gag
Hi

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, 07:27 PM
MATNTRNG
"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, 05:42 AM
running-gag
For instance
AE²=AB²+BE²=R²+(R-EF)²
• Jul 17th 2010, 01:02 PM
MATNTRNG
I got it! Thank you so much
• Jul 18th 2010, 09:57 AM
bjhopper
Hello MATNTRNG,
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.

bjh