# 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

$\Rightarrow$ AOB is a straight line

$\Rightarrow$ $\angle$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

$\\\angle ACB =\left ( \frac{1}{2} \right ) \angle AOB\\ \angle ACB =\left ( \frac{1}{2} \right ) 180^{\circ}\\ \angle ACB = 90^{\circ}$

$\Rightarrow$ ACB is a Right angle

So$\angle ABC$ follows Pythagoras theorem,

i.e., AB2 = AC2 + BC2

Therefore the given statement is true.

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