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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. Prove that O is equidistant from A, B and C.
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Solution
Draw lines AD and DC such that
AD || BC, AB || DC
Thus, AD = BC, AB=DC
The two right triangles △ABC and △ACD make a rectangle ABCD.
AC and BD are diagonals of the rectangle, so they are equal in length, and also bisect each other.
So, O is the equidistant from A, B, C and D.
Draw lines AD and DC such that
AD || BC, AB || DC
Thus, AD = BC, AB=DC
The two right triangles △ABC and △ACD make a rectangle ABCD.
AC and BD are diagonals of the rectangle, so they are equal in length, and also bisect each other.
So, O is the equidistant from A, B, C and D.
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