Question

1. if z is the circumcenter of △stu, sy = 19, tz = 21, and st = 30, find each measure. sz = ______ yu = ____ wt = ____ zy = ______

Explanation:

Step1: Recall property of circum - center

The circum - center of a triangle is equidistant from the vertices of the triangle. Since \(Z\) is the circum - center of \(\triangle STU\), \(SZ = TZ=UZ\). Given \(TZ = 21\), so \(SZ=21\).

Step2: Recall property of perpendicular bisector

The circum - center is the intersection of the perpendicular bisectors of the sides of the triangle. Since \(ZY\) is part of the perpendicular bisector of \(SU\), \(SY = YU\). Given \(SY = 19\), so \(YU = 19\).

Step3: Recall property of perpendicular bisector

Since \(ZW\) is part of the perpendicular bisector of \(ST\), \(WT=\frac{ST}{2}\). Given \(ST = 30\), so \(WT=\frac{30}{2}=15\).
We don't have enough information to find \(ZY\) with the given data.

Answer:

\(SZ = 21\)
\(YU = 19\)
\(WT = 15\)
\(ZY\): Insufficient data