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Question

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why Ois equidistant from A,B and C.


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Solution

Explaining why Ois equidistant from A,B and C:

Construction: Draw two lines AD and DC such that ADIIBC and ABIIDC

AD=BC,AB=DC

Since, ABCD is a rectangle.

Opposite sides are parallel and equal to each other and all the interior angles are right angles.

The property of rectangle states that the diagonals are of equal length and bisect each other.

Hence, AO=OC=BO=OD.

Therefore , O is equidistant from A,B and C.


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