Dante is incorrect because point P is not the circumcenter of the triangle.
What is the circumcenter of a triangle?
The circumcenter of a triangle is a specific point or location either inside or outside the triangle that represents the center if a circumcircle is drawn or if a circle that touches all the vertices of a triangle is drawn.
How to identify a circumcenter?
There are some simple characteristics to determine if a circumcenter is correct.
- All the vertices of a triangle have the same distance from the circumcenter.
- In obtuse triangles like the one shown in the image, this point is located outside the triangle.
Based on these characteristics we can conclude Dante is incorrect because the distance from point P to the three vertices is not the same and this point should be located outside not inside the triangle.
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