Q. 8

In Fig. 14.40, a right triangle BOA is given. C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices 0, A and B.


Answer :

Given that ∆BOA is right angled triangle


By midpoint formula,


x = , y =


For midpoint C on AB,


x =, y =


x = a and y = b


Coordinates of C are (a, b)


It is given that C is the midpoint of AB.


By distance formula,


XY =


For OC,


OC =


= …(1)


For AC,


AC =


=


As C is midpoint, AC = CB. …(2)


Hence from 1 and 2, we say that is point C is equidistant from the vertices 0, A and B.


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