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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 O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)
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Solution
ABCD is a rectangle as opposite sides are equal and parallel to each other, and all the interior angles are 90º.
In a rectangle, diagonals are of equal length and also these bisect each other.
Since MBC is right-angled at B. So ∠D = 90°, AD||BC and AB||DC
ABCD is a rectangle where AB = CD and AD=BC
AC and BD are the diagonals which bisect each other.
Hence, AO = OC = BO = OD
Thus, O is equidistant from A, B, and C.
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