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

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Solution

Produce BO to D such that $B O = O D$ . Join AD and DC. Then ABCD is a rectangle. In the rectangle ABCD, its diagonals AC and BD are equal and bisect each other at O,
$∴ O A = O C$ and $O B = O D$
But $A C = B D$
Therefore, $O A = O B = O C$
Thus, O is equidistant from $A, B a n d C .$

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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

Produce BO to D such that BO=OD. Join AD and DC. Then ABCD is a rectangle. In the rectangle ABCD, its diagonals AC and BD are equal and bisect each other at O,∴OA=OC and OB=ODBut AC=BDTherefore, OA=OB=OCThus, O is equidistant from A,B and C.

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

Produce BO to D such that $B O = O D$ . Join AD and DC. Then ABCD is a rectangle. In the rectangle ABCD, its diagonals AC and BD are equal and bisect each other at O,
$∴ O A = O C$ and $O B = O D$
But $A C = B D$
Therefore, $O A = O B = O C$
Thus, O is equidistant from $A, B a n d C .$