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Geometry - Parts of a Circle

Grade 5ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A circle is a closed curved shape where every point on the boundary is at the same distance from a fixed point called the center.

A circle showing the center point O.
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The Radius is the straight line distance from the center of the circle to any point on its boundary. It is denoted by rr.

A circle with a line segment from the center to the edge representing the radius.
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The Diameter is a straight line passing through the center, connecting two points on the boundary. It is the longest chord and its length is twice the radius (d=2×rd = 2 \times r).

A circle showing a diameter line passing through the center.
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A Chord is any line segment joining two points on the circle's boundary. The diameter is a special chord that passes through the center.

A circle showing a chord which is a line segment connecting two points on the boundary.
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An Arc is a part of the boundary (circumference) of the circle. The Circumference is the total boundary length of the circle.

📐Formulae

Diameter(d)=2×Radius(r)\text{Diameter} (d) = 2 \times \text{Radius} (r)

Radius(r)=Diameter(d)2\text{Radius} (r) = \frac{\text{Diameter} (d)}{2}

Diameter is the longest chord of a circle.\text{Diameter is the longest chord of a circle.}

💡Examples

Problem 1:

If the radius of a wooden ring is 8 cm8 \text{ cm}, find the length of its diameter.

Solution:

  1. Identify the given value: Radius (r)=8 cm(r) = 8 \text{ cm}.
  2. Use the formula: d=2×rd = 2 \times r.
  3. Substitute the value: d=2×8d = 2 \times 8.
  4. Calculate the result: d=16 cmd = 16 \text{ cm}.

Explanation:

Since the diameter is twice the length of the radius, we multiply the given radius by 22 to find the diameter.

Problem 2:

A circular clock has a diameter of 22 cm22 \text{ cm}. What is the radius of the clock?

Solution:

  1. Identify the given value: Diameter (d)=22 cm(d) = 22 \text{ cm}.
  2. Use the formula: r=d2r = \frac{d}{2}.
  3. Substitute the value: r=222r = \frac{22}{2}.
  4. Calculate the result: r=11 cmr = 11 \text{ cm}.

Explanation:

The radius is half the length of the diameter. To find the radius, we divide the diameter by 22.

Problem 3:

In a circle with center OO, a chord ABAB is drawn. If the radius of the circle is 5 cm5 \text{ cm}, find the length of the longest chord possible in this circle.

Diagram showing the diameter as the longest chord in a circle.

Solution:

  1. The longest chord of any circle is its diameter.
  2. Diameter (dd) = 2×Radius(r)2 \times \text{Radius} (r)
  3. Given r=5 cmr = 5 \text{ cm}
  4. d=2×5 cm=10 cmd = 2 \times 5 \text{ cm} = 10 \text{ cm} Therefore, the length of the longest chord is 10 cm10 \text{ cm}.

Explanation:

By definition, no chord can be longer than the diameter because the diameter passes through the widest part of the circle (the center).

Problem 4:

Calculate the radius of a circular park if the distance across the park through the center is 50 m50 \text{ m}.

Diagram of a circle with a diameter of 50m and a question mark for the radius.

Solution:

  1. The distance across the park through the center is the Diameter (dd).
  2. Given d=50 md = 50 \text{ m}.
  3. Radius (rr) = d2\frac{d}{2}
  4. r=502=25 mr = \frac{50}{2} = 25 \text{ m}. The radius of the park is 25 m25 \text{ m}.

Explanation:

Since the diameter is twice the radius, the radius is found by dividing the diameter by 2.