Write True or False and justify your answer.
The angles subtended by a chord at any two points of a circle are equal.

$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle APB = 130^{\circ}$,then find $\angle ACB$. (in $^{\circ}$)

In a circle with centre $P$,the length of a radius is $\sqrt{2} \ cm$. It is divided into two segments by chord $AB$ of length $2 \ cm$. If $C$ is a point on the major arc $AB$,then find the value of $\angle ACB$. (in $^{\circ}$)

In the given figure,if $\angle ABC = 45^{\circ}$,prove that $OA \perp OC$.

$A$ chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

$A$ circle has a radius of $\sqrt{2} \text{ cm}$. It is divided into two segments by a chord of length $2 \text{ cm}$. Prove that the angle subtended by the chord at a point in the major segment is $45^{\circ}$.