Question

Question 6
Write True or False and justify your answer :

If AOB is a diameter of a circle and C is a point on the circle, then $A{C}^2+B{C}^2=A{B}^2$

Answer 1

True

Any diameter of a circle subtends a right angle to any point on the circle.
If AOB is a diameter of a circle and C is a point on the circle, then $\Delta ACB$ is right angled at C.
In right-angled $\Delta ACB$, (use Pythagoras theorem)
$A{C}^2+B{C}^2=A{B}^2$