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CGP EDU Academic Team
Published on: August 14, 2026
If the circles x 2 + y 2 -10x + 16y + 89 - r 2 = 0 and x 2 + y 2 + 6x - 14y + 42 = 0 have common points, then the number of possible integral values of r is equal to
Text Solution
Verified by ExpertsThe correct answer is:
D
18
Centre & radius of x 2 + y 2 - 10x + 16y + 89 - r 2 = 0 are (5, -8) &| r| respectively
Centre & radius of x 2 + y 2 + 6x - 14y + 42 = 0 are (-3,7) & 4 respectively
Distance between the centres of circles is 
17-4 
|r| 
17 + 4
13 
r 
21
r 
{± 21, ±20, ±19, ±18, ±17, ±16, ±15, ±14, ±13}
Hence, the number of possible values of r is equal to 18
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