1. 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.

2. 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

3. "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

4. For instance
AE²=AB²+BE²=R²+(R-EF)²

5. I got it! Thank you so much

6. 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.

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