Question 3 of 50beginner🔧 ApplyShort Answer2 marks

What is the length of the longest chord in a circle of radius 5 units? Is there a smallest chord?

Correct Answer

The length of the longest chord is 10 units. There is no smallest chord.

Exercise: Think and Reflect | Q: 2 | (Page 3)
For More Understanding

Explanation

The provided context states that the diameter is the greatest chord because it contains the centre (its distance from the centre is zero). Therefore, the longest chord equals the diameter, which is twice the radius (2×52 \times 5 = 10 units). Regarding the smallest chord, the context explains that as a chord is pushed away from the centre, its length decreases until it becomes a single point with a length of zero. Thus, there is no single smallest chord of a fixed positive length.

Solution Steps

  1. Step 1: Identify that the longest chord in a circle is the diameter.

  2. Step 2: Calculate the diameter: Diameter = 2 × radius = 2×52 \times 5 = 10 units.

  3. Step 3: Determine if a smallest chord exists: As a chord is pushed away from the centre, its length decreases until it becomes a single point with length zero. Hence, there is no smallest chord.

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