Question

If y is the circumcenter is angle STU find each measure

Answer 1

Answer:

Measures are SV=9 units., SY=14 units, YW=$\sqrt75units$ , YW=$\sqrt27units$

Step-by-step explanation:

Given Y is the circumcenter of ΔSTU. we have to find the measures SV, SY, YW and YX.

As Circumcenter is equidistant from the vertices of triangle and also The circumcenter is the point at which the three perpendicular bisectors of the sides of the triangle meet.

Hence, VY, YW and YX are the perpendicular bisectors on the sides ST, TU and SU.

Given ST=18 units.

As VY is perpendicular bisector implies SV=9 units.

Also in triangle VTY

$YT^{2}=VY^{2}+VT^{2}$

⇒ $14^{2}=VY^{2}+9^{2}$

⇒ VY^{2}=115

As vertices of triangle are equidistant from the circumcenter

⇒ SY=YT=UY=14 units

Hence, SY is 14 units

In ΔUWY, $UY^{2}=YW^{2}+UW^{2}$

⇒ $14^{2}=YW^2+11^{2}$

⇒ $YW^2=196-121=75$ ⇒ YW=$\sqrt75units$

In ΔYXU, $UY^{2}=YX^{2}+XU^{2}$

⇒ $14^{2}=YX^2+13^{2}$

⇒ $YX^2=196-169=27$ ⇒ YW=$\sqrt27units$

Hence, measures are SV=9 units., SY=14 units, YW=$\sqrt75units$ , YW=$\sqrt27units$