Circles Question
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Grade 10 Circles CCSS: HSG-C.A.1
After increasing the radius of circle B, such that it is equal to the radius of circle A, how can we be sure that the two circles will lie exactly on top of each other?
- Since a circle is defined as a set of points a certain distance from a center, all the points on circle B will now be the same distance away from A as the points on circle A.
- Because a dilation is a rigid transformation, all the points on circle B must move by the same amount.
- Since the centers of the two circles are coincident, the rest of the circle must also be coincident.
- We can't be sure and need to use more radii from each circle to show this.