Circle A has a radius of 4 inches, and circle B has a radius of 6 inches. Prove that the two circles are similar.

Question

amistre64 · Answer

if their properties of perimeter and area and radius, differ by some constant scalar, wouldnt that fir the definition of similar?

mathstudent55 · Answer

Maybe you can prove it by showing that the circumferences are in the same ratio as the radii.

mathstudent55 · Answer

The areas differ by the square of the ratio of the radii and circumferences.

ranga · Answer

You can perform a translation so that the centers of circle A and circle B coincide.

A dilation of the circle with scale factor 6/4 or 3/2 takes the points of one circle and maps them on to the other.

Thus we have mapped one circle onto the other via a translation and a dilation.  So the circles are similar.