Question

IN ΔBCD line N is the perpendicular bisector of BC and line M is the perpendicular bisector of CD

which statement describes location of the circumcenter

A POINT 8
B the intersection of line M and CD
C the intersection of line N and BC
D the intersection of lines N and M

Answer 1

Correct answer is D(the intersection of lines N and M)

Explanation:

we Know that circumcenter of a triangle is point at which the perpendicular bisectors of the sides of a triangle intersect and which is equidistant from the three vertices. In other words circumcenter of a triangle is the center of the circle which passes through the vertices of the triangle. It means, any side of the triangle will act as a chord of the circumcircle. Hence the circumcenter of a triangle must lie on the perpendicular bisectors of the sides. therefore the intersection of line N and M must be circumcenter of the triangle.

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