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. [3 MARKS]
Concept: 0.5 Mark
Fig: 0.5 Mark
Solution: 2 Marks
If we extend BO to D, we get a rectangle ABCD. Now AC and BD are diagonals of the rectangle. In a rectangle diagonals are equal and bisect each other.
So, AC = BD
And,
AO = OC
BO = OD
Since AC = AO + CO = 2AO and BD = BO + DO = 2BO
We have,
AC = BD
⇒2AO= 2BO
⇒AO=BO
Therefore, AO = OC = BO = OD
So, it is clear that O is equidistant from A, B and C.