Finding the distance from the centroid to the vertex

Question: I i i i ii i i i ii i
Let ABC be a triangle where M is the midpoint of line AC, and line CN is the angle bisector of angle ACB with N on line AB. Let X be the intersection of the median BM and the bisector CN. In addition, triangle BXN is equilateral with AC=2. What is BX^2?

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Answered By:

Lainey E.
Passionate Math Teacher and Tutor 7-12 Grade Math

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Written Explanation:

This was a long involved process, but I found a formula someone had posted online that with an equilateral triangle your formula to find the distance from the centroid to the vertex is 2/3* (√3*x)/2 where x is the length of one of your triangle sides. And when I plug in 2 for x into that formula, I get the same answer as I did in the video so maybe that formula was taught to you and that's all you had to do in which case the process would've been a lot quicker. But that's a semi-longer way with the reasoning behind it (I had never seen that formula before so I'm not sure if you have). Hope this helped!

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