Consider triangle XYZ in the figure below.

Question

Consider triangle XYZ in the figure below. The perpendicular bisectors of its sides are TS, US, and VS. They meet at a single point S. (In other words, S is the circumcenter of triangle XYZ.) Suppose VS=72, YZ=80, and ZS=120. Find XS, UZ, and VY. Note that the figure is not drawn to scale.

Answer 1

Hi Sam!

I'll take a stab at this, but will make some assumptions

since there is no figure drawn.

I'm going to assume that the midpoint of XY is T, the

midpoint of YZ is U, and the midpoint of ZX is V.

The circumcenter is S. We know T,U, and V are

midpoints of the respective sides of the triangle

because a perpendicular bisector bisects the side

into two equal parts.

Since YZ = 80, we know that UZ will be half that. Why?

(Hint: perpendicular bisector bisects the side YZ into

two equal parts).

The distance from each of the vertices of the

triangle to the circumcenter S is the same.

You can use this information to find XS as well as

VY (have to figure in VS and YS to compute this).