Write True or False and justify your answer in each of the following: If AOB is a diameter of a circle and C is a point on the circle, then AC2 + BC2 = AB2.
True
Solution:
Given: AOB is a diameter of a circle
AOB is a straight line
AOB = 180°
Now, the angle subtended at the centre by an arc is twice the angle subtended by it at any part of the circle
ACB is a Right angle
So follows Pythagoras theorem,
i.e., AB2 = AC2 + BC2
Therefore the given statement is true.