George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct first step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.

Question

Olive Kim

Mathematics

22 October, 08:00

George is given two circles, Circle O and circle X, as shown. If he wants to prove that the two circles are similar, what would be the correct first step in his proof? Given: The radius of circle O is r, and the radius of circle X is r'. Prove: Circle O is similar to circle X.

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Bobo · Answer 1

Prove: Circle O is similar to circle x.

1. C=2*pi*r and C'=2*pi*r' by the definition of circumference

2. (C=2*pi*r) / (C'=2*pi*r') and C/C'=r/r' by the division of property of equality

3. d=2r and d'=2r by the definition of diameter

4. d=2r/d'=2r' and d/d'1=r/r' by the division property of equality

5. C/C'=d/d' and r/r'=r/r' by the substitution property

6. Circle 0 is similar to circle X, because all the linear dimensions are the same proportion

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