Answer: Option A. ->
:

The boundary of the circle is called its circumference and the value of circumference is $2\pi r\left(\text{where r is the radius of the circle}\right)$. If we cut a circle and form a line from it, then the length of the line will be the same as the circumference of the circle.

Answer: Option A. -> True
:
A

With three non-collinear points, only one circle can be drawn as shown below. Note the points should be non-collinear otherwise no circle can be drawn.

Answer: Option A. -> True
:

Only three tangents can be drawn passing through two external touching circles.

Answer: Option A. -> Diameter
:
A

A chord is a line which touches the circle at two distinct points on its circumference.
A segment is an area cut by a chord in a circle and hence cannot be a chord.
An arc is a part of the circumference and hence cannot be a chord.

The radius is not a chord as it does not touch the circle at two points on its circumference.

The diameter is a chord  since it touches the circle at two points on its circumference.

Answer: Option A. -> Diameter
:

Any line passing through the centre of the circle will perpendicularly bisect the chord of the circle.

Answer: Option A. ->  $(\frac{80}{2}{)}^{\circ }$
:
A and D

$\Delta AOB$ is an isosceles triangle (OA = OB; Radii),
$\Rightarrow \angle OAB=\angle OBA={50}^{\circ }.$
$\text{In}\Delta AOB,$
$\angle OAB+\angle OBA+\angle AOB={180}^{\circ }$
$\text{Hence,}\angle AOB={80}^{\circ }$

The angle subtended by an arc of the circle at its centre is double the angle subtended by it at any point on the remaining part of the circle.
Therefore, $\angle ACB=\frac{1}{2}\angle AOB={40}^{\circ }$.

Answer: Option D. -> ${90}^{\circ }$
:
D

An angle formed by the diameter of a circle at its circumference equals ${90}^{\circ }.$Hence, the value of $x$ is  ${90}^{\circ }$.

Answer: Option B. -> ${180}^{\circ }$
:
B

The opposite angles of a cyclic quadrilateral are supplementary to each other. Hence, the sum of opposite angles in a cyclic quadrilateral is ${180}^{\circ }$.

Answer: Option C. -> Infinite
:
C

An infinite number of circles can be drawn passing through two different points.
The line joining these two points can be the chord of an infinite number of circles having different radius.

Answer: Option C. -> Congruent arcs of a circle subtend right angles at the centre.
:
A, B, and D

(i) A perpendicular drawn from the centre of the circle acts as a perpendicular bisector to the chord.

(ii) Congruent arcs of a circle subtend equal angles at the centre. These angles are equal but not always a right angle. A right angle is subtended only when the arc is a semicircle.

(iii) Right angles will be subtended by congruent arcs only when they are semicircles.

(iv) If two chords are drawn at a same distance from the centre of a circle, they will be equal in length.