Question

Point S is the point of concurrency of the angle bisectors of ΔWXY.

Triangle W X Y is shown. Point S is the point of concurrency. Lines are drawn from each point of the triangle to point S. Lines are drawn from point S to the sides of the triangle to form right angles. Line segments S V, S U, and S T are formed.
What is SU?

SU = 5
SU = 7
SU = 12
SU = 13

Answer 1

I don't have the diagram or the side lengths, so I can't compute a numeric answer yet. A few facts that will let you (or me) finish it:

- S is the incenter, so SU, ST, and SV are all the same length (the inradius r).
- If the triangle's side lengths are a, b, c, compute the semiperimeter s = (a + b + c)/2 and the area Δ (e.g. by Heron's formula).
- Then r = SU = Δ / s.

If you post the picture or give the three side lengths (or enough other measures), I will compute SU and pick the correct choice.