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. [3 MARKS]

Answer 1

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
$\Rightarrow$2AO= 2BO
$\Rightarrow$AO=BO

Therefore, AO = OC = BO = OD

So, it is clear that O is equidistant from A, B and C.