Question:
The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is:
The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is:
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Use the geometric properties of intersecting circles to calculate the length of common chords.
Updated On: Aug 4, 2025
- 24 cm
- 25 cm
- 15 cm
- 20 cm
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The Correct Option is B
Solution and Explanation
Using the formula for the length of the common chord of two intersecting circles:
\[
L = 2 \sqrt{r_1^2 - d^2}
\]
Where \( r_1 = 20 \) cm (radius of the larger circle), \( r_2 = 15 \) cm (radius of the smaller circle), and \( d = 25 \) cm (distance between the centers). The length of the common chord is:
\[
L = 2 \sqrt{20^2 - 25^2} = 2 \sqrt{400 - 625} = 25 \, \text{cm}
\]
Thus, the length of the common chord is 25 cm.
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