Question 35 of 50beginner🔧 ApplyNumerical3 marks

The distance of a chord of length 16 cm from the centre of a circle is 6 cm. Find the radius of the circle.

Correct Answer

We are given that the chord length is 16 cm and its distance from the centre (d) is 6 cm. According to the relation provided, the chord length is given by the formula 2r2−d22\sqrt{r^2 - d^2}, where rr is the radius of the circle.

Substituting the given values into the formula, we get: 16 = 2r2−622\sqrt{r^2 - 6^2} 8 = r2−36\sqrt{r^2 - 36}

Squaring both sides to eliminate the square root, we find: 64 = r2−36r^2 - 36 r2r^2 = 64 + 36 = 100

Therefore, the radius of the circle is rr = 10 cm.

Exercise: END-OF-CHAPTER EXERCISES | Q: 9 | (Page 23)
For More Understanding

Explanation

The textbook context provides the formula relating chord length, radius, and perpendicular distance from the centre as: Chord length = 2r2−d22\sqrt{r^2 - d^2}. Given the chord length is 16 cm and the distance from the centre (d) is 6 cm, we substitute these values into the formula to solve for the radius (r).

Solution Steps

  1. Given: Chord length = 16 cm, Distance from centre (d) = 6 cm

  2. Formula: Chord length = 2r2−d22\sqrt{r^2 - d^2}

  3. Substitute values: 16 = 2r2−622\sqrt{r^2 - 6^2}

  4. Simplify: 8 = r2−36\sqrt{r^2 - 36}

  5. Square both sides: 64 = r2−36r^2 - 36

  6. Solve for r: r2r^2 = 64 + 36 = 100, so r = 10 cm

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