Describe a dilation that maps one circle to another when the circles have the same center
Problem
Circle \(A\): center \(O\) radius \(4\); Circle \(B\): same center \(O\) radius \(10\). Describe a dilation that maps Circle \(A\) to Circle \(B\).
Big Picture
What this problem is really about
When two circles share a center, that common point is the natural fixed point of the dilation. We’ll form the target-to-source radius ratio, check whether it enlarges or reduces, and verify that every source radius is sent to the target radius along the same ray.
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