Question

If z is the circumcenter of triangle qrs find each measure

Answer 1

Answer:

Step-by-step explanation:

Circumcenter of A triangle is the center of a circle passing through the vertices of the given triangle.

So, the distance of Z from the vertices Q, R and S will be the radii of the circle.

Therefore, ZQ = ZR = ZS

Since, circumcenter of a triangle is defined by the point of intersection of the perpendicular bisectors of the sides of the given triangle.

Therefore, points W, X and Y are the midpoints of sides QR, RS and QS.

Using these facts,

a). QR = 2(WQ)

          = 2(25)

          = 50

b). Apply Pythagoras theorem in ΔRXZ,

    (RZ)² = (RX)² + (ZX)²

    (RZ)² = (40)² + (9)²

     RZ = √1681 = 41

c). XS = $\frac{1}{2}(RS)$

          = $\frac{1}{2}(80)$

          = 40

d). Since, ZQ = ZR = ZS

    ZS = 41

e). By applying Pythagoras theorem in ΔRWZ,

   (RZ)² = (WZ)² + (WR)²

   (41)² = (WZ)² + (25)²

   (WZ)² = (41)² - (25)²

    WZ = √1056

   WZ = $4\sqrt{66}$

          ≈ 32.5