Mathematics
Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcenter of the ΔDEF.
Statement 2: The incenter of a triangle is the point where the bisector of the angles intersects.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
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Answer
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides intersect. It is equidistant from the three vertices (D, E, and F) of the triangle.
∴ Statement 1 is true.
The incenter of a triangle is defined as the point of concurrency of the three angle bisectors of the triangle. This point is also the center of the inscribed circle and is equidistant from the three sides of the triangle.
∴ Statement 2 is true.
∴ Both statements are true.
Hence, option 1 is the correct option.
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