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Leya [2.2K]
3 years ago
6

Fint the center circle with these coordnates (10,3)(3,10)and(-4,3

Mathematics
1 answer:
omeli [17]3 years ago
4 0
The length of the line joining the center of the circle and each coordinate is equal.
Let the center of the circle be (a, b), then
(a - 10)^2 + (b - 3)^2 = (a - 3)^2 + (b - 10)^2 = (a + 4)^2 + (b - 3)^2
a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 - 6a + 9 + b^2 - 20b + 100 = a^2 + 8a + 16 + b^2 - 6b + 9

a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 - 6a + 9 + b^2 - 20b + 100 . . . (1)
a^2 - 20a + 100 + b^2 - 6b + 9 = a^2 + 8a + 16 + b^2 - 6b + 9 . . . (2)

From (1): 14a - 14b = 0 => a = b
From (2): 28a = 84 => a = 84/28 = 3

Therefore, center = (a, b) = (3, 3)
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