Question 22 of 50beginner🔧 ApplyNumerical3 marks

Find the length of the chord of a circle where the radius is 7 cm and perpendicular distance is 6 cm.

Correct Answer

To find the length of the chord, we use the property that the perpendicular from the centre of a circle to a chord bisects the chord. This forms a right-angled triangle where the radius is the hypotenuse, the perpendicular distance is one leg, and half the chord is the other leg. The formula for the chord length is 2r2−d22\sqrt{r^2 - d^2}.

Given: Radius (rr) = 7 cm, Perpendicular distance (dd) = 6 cm. Step 1: Substitute the values into the formula: Length of chord = 272−622\sqrt{7^2 - 6^2} Step 2: Calculate the squares: Length of chord = 249−362\sqrt{49 - 36} Step 3: Subtract the values: Length of chord = 2132\sqrt{13}

Therefore, the length of the chord is 2132\sqrt{13} cm.

Exercise: Exercise Set 5.5 | Q: 1 | (Page 14)
For More Understanding

Explanation

The textbook context provides the formula for the length of a chord given its perpendicular distance from the centre and the radius: 2r2−d2\sqrt{r² - d²}. It also states Theorem 5, which establishes that the perpendicular from the centre bisects the chord, allowing the use of the Pythagorean theorem to derive this formula.

Solution Steps

  1. Step 1: Identify given values: Radius (r) = 7 cm, Perpendicular distance (d) = 6 cm.

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

  3. Step 3: Substitute the values: 272−62\sqrt{7² - 6²} = 249−36\sqrt{49 - 36} = 213\sqrt{13} cm.

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