SOLUTION: The three medians of right triangle ABC intersect at G as shown. Given than AC = 8, AB = 15, what is CG?

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Question 1195770: The three medians of right triangle ABC intersect at G as shown. Given than AC = 8, AB = 15, what is CG?
Found 2 solutions by lotusjayden, ikleyn:
Answer by lotusjayden(18) About Me  (Show Source):
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Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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The median CF is the hypotenuse of the right triangle ACF; therefore

    |CF| = sqrt%288%5E2+%2B+%2815%2F2%29%5E2%29%29 = sqrt%288%5E2+%2B+7.5%5E2%29 = sqrt%2864+%2B+56.25%29 = sqrt%28120.25%29.


About the medians of any triangle, the widely known fact is that they intersect in one common point and
this intersection point divides each median in proportion 2:1, counting from the vertex of the triangle.


THEREFORE,  |CG| = %282%2F3%29%2Asqrt%28120.25%29 = 7.311, rounded with 3 decimal places.    ANSWER

Solved.