Circles (Basic properties)：練習問題

What do we call the line segment that joins the centre of a circle to any point on its circumference?

Which of the following descriptions about a sphere is correct?

In the figure below, the radius of Circle \(A\) is \(8\text{ cm}\), the radius of Circle \(B\) is \(5\text{ cm}\), and the radius of Circle \(C\) is \(3\text{ cm}\). The three circles touch each other externally in a straight line as shown. What is the distance between the centre of Circle \(A\) and the centre of Circle \(C\)?

Which of the following is a basic property of a circle?

In circle \(O\), the diameter \(AB\) passes through the centre. If the length of the radius is \(r\), and a line segment \(XY\) connects two points on the circle but does not pass through the centre, which of the following is true about its length?

The radius of a circular clock face is \(10\) cm. What is the length of the diameter of this clock face in cm?

Explain how the distance from any point on the surface of a sphere to its center relates to the sphere's radius.

In the figure below, two identical circles each with radius \(5\text{ cm}\) touch each other. A rectangle is drawn tightly enclosing both circles side by side. Find the perimeter of the rectangle.

A circular garden has a diameter of \( 14 \) metres. A straight path is built connecting two points on the edge of the circle.

(a) What is the length of the longest possible straight path that can be built inside this garden?
(b) Calculate the radius of the circular garden.
(c) If a person walks exactly one round along the edge of the garden, how far do they walk? (Use \( \pi = \frac{22}{7} \))

In the figure below, two concentric circles share the same centre \(O\). The diameter of the smaller circle is \(12\text{ cm}\), and the width of the ring (the distance between the two circular boundaries) is \(4\text{ cm}\).
(a) Find the radius of the smaller circle.
(b) Find the radius of the larger circle.
(c) Find the diameter of the larger circle.
(d) A line segment passes through \(O\) and has both endpoints on the larger circle's circumference. What is the name and length of this line segment?