Question 30 of 50beginner🔧 ApplyNumerical3 marks

A circle has a radius of 15 cm. A chord is drawn. The distance from the centre of the circle to the chord is 9 cm. What is the length of the chord?

Correct Answer

24 cm

Exercise: END-OF-CHAPTER EXERCISES | Q: 4 | (Page 23)
For More Understanding

Explanation

The textbook context provides the formula for the length of a chord as 2r2−d2\sqrt{r² - d²}, where r is the radius and d is the perpendicular distance from the centre to the chord. Substituting r = 15 cm and d = 9 cm gives 2152−92\sqrt{15² - 9²} = 2225−81\sqrt{225 - 81} = 2144\sqrt{144} = 2 * 12 = 24 cm.

Solution Steps

  1. Step 1: Identify the given values: Radius (r) = 15 cm, Perpendicular distance from centre (d) = 9 cm.

  2. Step 2: Apply the chord length formula: Chord length = 2r2−d2\sqrt{r² - d²}.

  3. Step 3: Substitute the values into the formula: 2152−92\sqrt{15² - 9²} = 2225−81\sqrt{225 - 81} = 2144\sqrt{144}.

  4. Step 4: Calculate the final length: 2×122 \times 12 = 24 cm.

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