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.

Answers (1)

True

Solution:

Given: AOB is a diameter of a circle

\Rightarrow AOB is a straight line

\Rightarrow \angleAOB = 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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