Fill in the blanks and select the correct option .
(I) There is (are) __P__ circle (s) passing through three non-collinear points .
(II) A continuous piece of a circle is called the __Q__ of the circle .
(III) If two arcs of a circle are congruent then their corresponding chords are __R__ .
(IV) A line segment joining the centre to any point on the circle is called its __S__ .
(V) The sum of either pair of opposite angles of a cyclic quadrilateral is __T__ .

Options

A. `{:(P,Q,R,S,T),("Infinite","Chord","Not equal","Diameter",360^(@)):}`
B. `{:(P,Q,R,S,T),("Two","Arc","Equal","Diameter",360^(@)):}`
C. `{:(P,Q,R,S,T),("One","Chord","Equal","Radius",180^(@)):}`
D. `{:(P,Q,R,S,T),("One","Arc","Equal","Radius",180^(@)):}`

Answer

Let's solve the question step by step.

### Step 1: Identify the number of circles passing through three non-collinear points.
- **Statement**: There is (are) __P__ circle(s) passing through three non-collinear points.
- **Solution**: There is **one** circle passing through three non-collinear points.
- **Answer**: P = one

### Step 2: Define a continuous piece of a circle.
- **Statement**: A continuous piece of a circle is called the __Q__ of the circle.
- **Solution**: A continuous piece of a circle is called the **arc** of the circle.
- **Answer**: Q = arc

### Step 3: Determine the relationship between congruent arcs and their corresponding chords.
- **Statement**: If two arcs of a circle are congruent then their corresponding chords are __R__.
- **Solution**: If two arcs of a circle are congruent, then their corresponding chords are **equal**.
- **Answer**: R = equal

### Step 4: Define the line segment from the center to any point on the circle.
- **Statement**: A line segment joining the centre to any point on the circle is called its __S__.
- **Solution**: A line segment joining the center to any point on the circle is called its **radius**.
- **Answer**: S = radius

### Step 5: State the sum of opposite angles in a cyclic quadrilateral.
- **Statement**: The sum of either pair of opposite angles of a cyclic quadrilateral is __T__.
- **Solution**: The sum of either pair of opposite angles of a cyclic quadrilateral is **180 degrees**.
- **Answer**: T = 180 degrees

### Final Answers:
- P = one
- Q = arc
- R = equal
- S = radius
- T = 180 degrees