Question

The perpendicular distance from the centre of a circle to a chord of length 8 cm is 3 cm. Then the radius of the circle is:

• A. 4 cm
• B. 5 cm
• C. 10 cm
• D. 8 cm

Hint:

Use the Pythagorean theorem for right triangles formed by the radius, perpendicular, and half of the chord to find the radius.

Answer 1

The Correct Option is B

Let the radius of the circle be \( r \), and the perpendicular distance from the centre to the chord be \( d = 3 \) cm. The length of the chord is \( 8 \) cm. In the right triangle formed by the radius, the perpendicular, and half of the chord, we apply the Pythagorean theorem. Half of the chord is \( 4 \) cm. Thus, we have: \[ r^2 = 4^2 + 3^2 = 16 + 9 = 25 \quad \Rightarrow \quad r = \sqrt{25} = 5 \text{ cm}. \] Therefore, the radius of the circle is \( \boxed{5} \text{ cm} \).