Question

A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.

• A. 2.5 cm
• B. 2.4 cm
• C. 3.5 cm
• D. 3 cm

Hint:

When solving problems with chords and circles, use the Pythagorean theorem to relate the radius, perpendicular distance, and half the length of the chord.

Answer 1

The Correct Option is C

Step 1: Use the chord length and perpendicular distance.
For any circle, the perpendicular from the center of the circle to a chord bisects the chord. Thus, if the length of the chord is \( 2a \) and the distance from the center is \( d \), the radius \( r \) of the circle can be found using the Pythagorean theorem: \[ r^2 = a^2 + d^2. \] We are given that the length of the first chord is 6 cm and its perpendicular distance from the center is 4 cm. For this chord, we have: \[ r^2 = 3^2 + 4^2 = 9 + 16 = 25 $\Rightarrow$ r = 5 \text{ cm}. \]

Step 2: Use the radius for the second chord.
Now, for the second chord, we have a chord length of 8 cm, so \( 2a = 8 \) and \( a = 4 \). Using the Pythagorean theorem again, the distance from the center is \( d \): \[ 5^2 = 4^2 + d^2. \] \[ 25 = 16 + d^2 $\Rightarrow$ d^2 = 9 $\Rightarrow$ d = 3 \text{ cm}. \]

Step 3: Conclusion.
The correct answer is (C) 3.5 cm.