Question 1193673
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From the given information, we know that the two angle bisectors meet at R; and we know that the distance from each vertex to R is 8.<br>
In a triangle, the three angle bisectors meet so that each bisector is divided into two lengths in the ratio 2:1; that makes the altitude of the triangle 8+4=12.<br>
Then the ratio of the lengths of the altitude and side of an equilateral triangle is sqrt(3):2, so the side length of the triangle is {{{12(2/sqrt(3))=24/sqrt(3)=8*sqrt(3)}}}<br>
ANSWER: NQ=8*sqrt(3)<br>