In below figure, a right triangle BOA is given. C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.

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Solution

C is midpoint of AB,
Coordinates of C = $left parenthesis fraction numerator 0 plus 2 a over denominator 2 end fraction comma fraction numerator 2 b plus 0 over denominator 2 end fraction right parenthesis equals left parenthesis a comma b right parenthesis$
CA =
CB =
OC =

Clearly CA = CB = OC
Hence C is equidistant from A, B and O.

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