Amazing center of an amazing circle

Geometry Level 4

Then the centre of the circle is:

(-2,2.5) Data is inconsistent Data insufficient (2,2.5)

1 solution

Roman Frago
Feb 21, 2015

If $f(x,0)=0$ has both roots equal to 2, it suggests that the y-coordinate of the center is $0$ . This contradicts the statement " $f(0,y)=0$ has 2 and 3 as its roots" as this suggests that the y-coordinate of the center is $\frac {5} {2}$ .

The first condition implies that the x-coordinate of centre is 2. so c=4. but for second condition product of roots must be 4 which contradicts the given data

Ťånåy Nårshånå - 6 years, 3 months ago

This is correct, I misinterpreted the first condition. The x-coordinate of the center is 2. With the center at $(2,\frac {5} {2})$ , points (2,0), (0,3), (0,2) do not belong to the same circle as they are not equidistant from the center.

Edit: There would have 2 concentric circles.

Roman Frago - 6 years, 3 months ago

Amazing center of an amazing circle

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