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Question 148388: what is the equation for the circumscribed circle whose triangle verticies are A = (-5,12), B = (5, -12), and C = (5,12)?
thanks
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! A and C have the same y coordinate (12), so AC is a vertical line
B and C have the same x coordinate (5), so BC is a horizontal line
AC and BC are perpendicular, so ABC is a right triangle
__ this means that the hypotenuse (AB) is the diameter of the circumscribed circle
the center of the circle is the midpoint of AB __ (5-5)/2 and (12-12)/2 __ (0,0) or the origin
the radius of the circle is the distance from the center to either A or B
__ by Pythagoras, r^2=(-5)^2+12^2 __ r^2=169 __ r=13
so the equation of the circle is (x-0)^2 + (y-0)^2 = 13^2 __ x^2+y^2=169
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