Question

\(ABC\) is a right-angled triangle and \(O\) is the mid point of the side opposite to the right angle. Explain why \(O\) is equidistant from \(A, B\) and \(C\). (The dotted lines are drawn additionally to help you).

Answer 1

Draw lines \(AD\) and \(DC\) such that \(AD||BC\), \(AB||DC\)
\(AD = BC\), \(AB = DC\)
\(ABCD\) is a rectangle as opposite sides are equal and parallel to each other and all the interior angles are of \(90\degree\).
In a rectangle, diagonals are of equal length and also these bisect each other.
Hence, \(AO = OC \) = \(BO = OD\)

Thus, \(O\) is equidistant from \(A, B\), and \(C\).