Two congruent circles with centres at (2,3) and (5,6), which intersect at right angles, have radius equal to?

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Cailyn Knight · Accepted Answer

Circles naturally cross at a 90 degree angle.  Given that circles have the same radius, they are congruent.  Then         r     1      =        r     2      =   r           C     1           C     2      =        (     5     &amp;#x2212;     2            )       2          +     (     6     &amp;#x2212;     3            )       2                   C     1           C     2      =        18      By pythagoros theorem          r     2      +        r     2      =   (        C     1           C     2           )     2         &amp;#x21D2;   2        r     2      =   (        18           )     2         &amp;#x21D2;        r     2      =   9      &amp;#x21D2;   r   =   3

Two congruent circles with centres at (2,3) and (5,6), which intersect at right angles, have radius equal to?

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