The circumcentre is always equally distant from all three vertices of a triangle. Therefore, OA, OB and OC are equal. Small differences may appear only because of minor drawing or measuring errors.
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The triangle formed is an obtuse-angled triangle. In every obtuse-angled triangle, the circumcentre lies outside the triangle. Therefore, the centre of the circumcircle is outside the triangle.
The triangle formed is an acute-angled triangle. In every acute-angled triangle, the circumcentre lies inside the triangle. Therefore, the centre of the circumcircle is located inside the triangle.
Rearranging the conditional constraint gives x – 2y – 6 = 0. The polynomial can be formatted as x cube + (-2y) cube + (-6) cube – 3(x)(-2y)(-6), which evaluates directly to 0 because the base sum is 0.
The expression matches the identity form of a cube + b cube + c cube – 3abc where a = x, b = y and c = 4. Since the sum a + b + c equals 0, the entire ...