State whether the following statement is True or False and justify your answer: If $AOB$ is a diameter of a circle and $C$ is a point on the circle,then $AC^{2} + BC^{2} = AB^{2}$.
(A) $AOB$ is a diameter of a circle and $C$ is a point on the circle.
Since the angle in a semicircle is a right angle,$\angle ACB = 90^{\circ}$.
In the right-angled triangle $\Delta ABC$,by applying the Pythagoras theorem:
$AC^{2} + BC^{2} = AB^{2}$.
Therefore,the given statement is True.
Since the angle in a semicircle is a right angle,$\angle ACB = 90^{\circ}$.
In the right-angled triangle $\Delta ABC$,by applying the Pythagoras theorem:
$AC^{2} + BC^{2} = AB^{2}$.
Therefore,the given statement is True.
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