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In below Fig. 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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Given a right triangle BOA with vertices B(0,2b), O(0,0), A(2a,0)

Since, C is the midpoint of AB

Therefore, coordinates of C are


Since, CO=CA =CB

Therefore, C is equidistant from O, A and B

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