question_answer 31)

                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:

                Construction: Produce BO to D such that BO = OD. Join AD and CD.     Proof. \[\overline{AD}||\overline{BC}:\,\,\overline{AB}||\overline{DC}\]. So in parallelogram ABCD, the midpoint of the diagonal \[\overline{AC}\] is O. Hence, O is equidistant from A, B and C.