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¯¯¯¯¯¯ , EG¯¯¯¯¯ , and FG¯¯¯¯¯ are perpendicular bisectors of the sides of △ABC . BE=3 cm and GE=4 cm.

What is AG ?

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cm
Triangle A B C with three dashed lines drawn that intersect at point G. Line D G is perpendicular to side A B. Line E G is perpendicular to side B C. Line F G is perpendicular to side A C. Segment A G, segment B G and segment C G are drawn.

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If triangle ABC is an equilateral triangle, then this can be solved easily. Given this layout, triangle BEG is a right triangle. Therefore using the pythagorean theorem, the length of the hypotenuse, BG, is sqrt(3^2 + 4^2) => sqrt(25) = 5cm. If triangle ABC is equilateral, then the length of bisector BF is equal to the length of bisector AE, and the length of BG is equal to the length of AG, so segment AG = 5cm.
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Answer:

What is AG? 5 cm

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