Find the length of common chord if radii of two intersecting circles are 120…
2024
Find the length of common chord if radii of two intersecting circles are 120 and 160 given , distance between two centre are 200.
- A.
190
- B.
192
- C.
196
- D.
200
Attempted by 191 students.
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Correct answer: B
We are given two circles with radii r1 = 120, r2 = 160 and centre distance d = 200. Find the length of their common chord.
Let x be the distance from the centre of the first circle (radius 120) to the midpoint of the common chord along the line joining the centres. Then
x = (r1^2 - r2^2 + d^2) / (2d). Substitute values:
x = (120^2 - 160^2 + 200^2) / (2*200) = (14400 - 25600 + 40000)/400 = 28800/400 = 72.
Half the common chord = sqrt(r1^2 - x^2) = sqrt(120^2 - 72^2) = sqrt(14400 - 5184) = sqrt(9216) = 96.
Full common chord = 2 * 96 = 192.
Quick check: because 120^2 + 160^2 = 200^2, the expression simplifies and the chord can be computed directly using chord = 2*r1*r2/d = 2*120*160/200 = 192.