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Sides of an obtuse triangle AB, BC, and AC have midpoints E, F, and D. G is the point of intersection of all 3 medians.

If AB = 7, BC = 9, and BG = 3 then what's the length of AC? (AC is the longest side)

 Nov 17, 2020
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Sides of an obtuse triangle AB, BC, and AC have midpoints E, F, and D. G is the point of intersection of all 3 medians.

If AB = 7, BC = 9, and BG = 3 then what's the length of AC? (AC is the longest side)

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The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.

 

If BG is 3 then BD = 3 * 1.5 = 4.5

 

Since we have: AB=7,  BC=9, and BD=4.5 we can use  Apollonius's theorem to find AC.

 

|AB|2 + |BC|2 = 2( |AD|2 + |BD|2 )

 

AC = 2|AD|  ≈ 13.379

 

 Nov 18, 2020

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