I would say that it would maby be (c)
Answer:
Circumcenter = (4,0)
Circumcircle = √5
Step-by-step explanation:
The circumcentre is the point of intersection of the perpendicular bisectors of a triangle. The vertices of the triangle are equidistant to the circumcentre.
Let us assume the coordinate of the circumcentre is at O(x, y). Therefore the distance between the cirmcumcenter and the vertices are:
![AO=\sqrt{(x-2)^2+(y-1)^2} =\sqrt{x^2-4x+4+(y^2-2y+1)}\\=\sqrt{x^2+y^2-4x-2y+5} \\\\BO=\sqrt{(x-5)^2+(y-2)^2} =\sqrt{x^2-10x+25+(y^2-4y+4)}\\=\sqrt{x^2+y^2-10x-4y+29} \\\\CO=\sqrt{(x-3)^2+(y-4)^2} \\=\sqrt{x^2-9x+9+(y^2-8y+16)}=\sqrt{x^2+y^2-9x-8y+25} \\](https://tex.z-dn.net/?f=AO%3D%5Csqrt%7B%28x-2%29%5E2%2B%28y-1%29%5E2%7D%20%3D%5Csqrt%7Bx%5E2-4x%2B4%2B%28y%5E2-2y%2B1%29%7D%5C%5C%3D%5Csqrt%7Bx%5E2%2By%5E2-4x-2y%2B5%7D%20%20%5C%5C%5C%5CBO%3D%5Csqrt%7B%28x-5%29%5E2%2B%28y-2%29%5E2%7D%20%3D%5Csqrt%7Bx%5E2-10x%2B25%2B%28y%5E2-4y%2B4%29%7D%5C%5C%3D%5Csqrt%7Bx%5E2%2By%5E2-10x-4y%2B29%7D%20%20%5C%5C%5C%5CCO%3D%5Csqrt%7B%28x-3%29%5E2%2B%28y-4%29%5E2%7D%20%5C%5C%3D%5Csqrt%7Bx%5E2-9x%2B9%2B%28y%5E2-8y%2B16%29%7D%3D%5Csqrt%7Bx%5E2%2By%5E2-9x-8y%2B25%7D%20%20%5C%5C)
AO = BO, therefore
√(x² + y²-4x-2y+5) = √(x² + y² - 10x - 4y + 29)
x² + y²-4x-2y+5 = x² + y² - 10x - 4y + 29
6x + 2y = 24 (1)
BO = CO
√(x² + y² - 10x - 4y + 29) = √(x² + y² - 9x - 8y + 25)
x² + y² - 10x - 4y + 29 = x² + y² - 9x - 8y + 25
-x + 4y = -4 (2)
Multiply equation 2 by 6 and add to equation 1:
26y = 0
y=0
Put y = 0 in -x + 4y = -4
-x + 4(0) = -4
x = 4
The cicumcenter is at (4, 0)
The radius of the circumcircle = AO = BO = CO. Therefore:
![Radius=AO=\sqrt{(4-2)^2+(0-1)^2} =\sqrt{4+1}=\sqrt{5}](https://tex.z-dn.net/?f=Radius%3DAO%3D%5Csqrt%7B%284-2%29%5E2%2B%280-1%29%5E2%7D%20%3D%5Csqrt%7B4%2B1%7D%3D%5Csqrt%7B5%7D)
Answer:
Step-by-step explanation:
See attached file for answer .
Following order of operations:
3^2 = 9
(10-2) = 8
Now you have :
9 + 8 x 5 -4
Multiplication is next:
9 + 40 -4
Now just add and subtract from left to right:
9 + 40 = 49
49-4 = 45
The answer is 45
Generally in the US a ton is approximately 907 kilograms and a metric ton is equivalent to 1,000 kilograms