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 $\angle ACB = 50^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

$ABCD$ is a cyclic quadrilateral in which $\angle BAC = 45^{\circ}$ and $\angle ADB = 55^{\circ},$ then $\angle ABC = \dots$ (in $^{\circ}$)

State whether each of the following statements is true or false:
$(1)$ $A$ line segment joining any two points of a circle is a diameter of the circle.
$(2)$ For any circle, $\text{diameter} = 2 \times \text{radius}$.
$(3)$ In a circle with radius $14 \text{ cm}$, the length of a chord can be $32 \text{ cm}$.

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 $^{\circ}$)

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 $AC^{2} + BC^{2} = AB^{2}$.