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Which theorem explains why the circumcenter is equidistant from the vertices of a triangle

A - vertical angles theorem
B - concurrency of perpendicular bisectors theorem
C - concurrency of angle bisector theorem
D - alternate interior angles theorem

User Shinil
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2 Answers

3 votes

Answer:

B

Explanation:

TRUST

User Ahumesky
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The answer is B. Remember the definition of the circumcenter of a triangle: the intersection of perpendicular bisectors. If we draw a perpendicular line to each of the three sides, these three lines intersect at a common point, and the distance of this point to all three vertices are equal, which can be proved using similar triangles. If we draw a circle with the circumcenter of the triangle as the center, and with the distance from circumcenter to vertices as the radius, the triangle will become inscribed in the circle.
User Collie
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