The perpendicular bisectors of triangle ABC intersect at point G and are shown in blue. Find BG

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03-11-2022
Mathematics

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The perpendicular bisectors of triangle ABC intersect at point G and are shown in blue. Find BG

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DerellR540388 DerellR540388 · Answer 1 · 2022-11-03T11:35:21+01:00

Answer:

9

Explanation:

A perpendicular bisector of a triangle is a line that is perpendicular to the side and passes through the midpoint of the triangle.

So when three perpendicular bisectors of the sides of a triangle meet at a point in a triangle, that point is called a circumcenter.

From the circumcenter theorem, we know that the circumcenter is equidistant from the vertices of a triangle, that is, the circumcenter is the same distance from each of the vertices of the triangle.

Looking at the given triangle, we can see that G is the circumcenter of the triangle because all the perpendicular bisectors DG, EG, and FG meet at this point.

We can see that AG is 9 which is the distance from vertex A to the circumcenter, G, since the circumcenter is equidistant from the vertices of a triangle according to the circumcenter theorem, therefore, BG will also be 9.