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Question -

In the 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.



Answer -


In right ∆OAB, co-ordinates of O are (0, 0) of A are (2a, 0) and of B are (0, 2b)
C is the mid-point of AB
Co-ordinates of C will be
We see that CO = CA = CB
Hence C is equidistant from the vertices O, A and B.
Hence proved.

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