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ABC is an isosceles triangle. If AB =AC =16, BC=8. D is the midpoint of side AC , and G is the centroid of triangle ABC , find BD .

draw the altitude from A to form a right-angled triangle.
Cos C = 4/16 = 1/4

In triangle BCD, by the cosine law ...
BD^2 =8^2 + 8^2 - 2(8)(8)cosC
= 64 +64 - 128(1/4)
= 160
BD = √160 = 4√10

Where does the centroid G enter the picture?

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