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:
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:
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Use the Pythagorean theorem for right triangles formed by the radius, perpendicular, and half of the chord to find the radius.
Updated On: Oct 27, 2025
- 4 cm
- 5 cm
- 10 cm
- 8 cm
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The Correct Option is B
Solution and Explanation
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 \( \boxed{5} \text{ cm} \).
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