Question 29 of 50beginner🔧 ApplyNumerical3 marks

The diameter of a circle is 26 cm. A chord of length 24 cm is drawn in the circle. Find the distance from the centre of the circle to the chord.

Correct Answer

5 cm

Exercise: END-OF-CHAPTER EXERCISES | Q: 3 | (Page 23)
For More Understanding

Explanation

The question requires finding the perpendicular distance from the centre to a chord. According to Theorem 5 from the provided context, the perpendicular from the centre of a circle to a chord bisects the chord. This creates a right-angled triangle where the radius is the hypotenuse, and the perpendicular distance and half the chord length are the legs. Using the Pythagorean theorem, the distance can be calculated.

Solution Steps

  1. Step 1: Calculate the radius of the circle. Radius (r) = Diameter / 2 = 26 / 2 = 13 cm.

  2. Step 2: Apply Theorem 5, which states that the perpendicular from the centre of a circle to a chord bisects the chord. So, half the length of the chord = 24 / 2 = 12 cm.

  3. Step 3: Use the relationship r² = d² + (chord/2)², where d is the perpendicular distance from the centre to the chord. Substituting the values: 13² = d² + 12².

  4. Step 4: Solve for d. 169 = d² + 144, which gives d² = 25. Taking the square root, d = 5 cm.

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