Question

The perpendicular bisectors of its sides are SV, TV, and UV. They meet at a single point V. (In other words, V is the circumcenter of APQR.) Suppose UV=48, PS= 62, and RV 80. Find PU, PR, and QV. Note that the figure is not drawn to scale.​

Answer 1

To find PU, PR, and QV, we can use the properties of perpendicular bisectors in a triangle. The perpendicular bisectors of the sides of APQR meet at the circumcenter V. By setting up equations based on the lengths given, we can solve for the values of PU, PR, and QV.

Step-by-step explanation:

To find PU, PR, and QV, we can use the properties of perpendicular bisectors in a triangle.

The perpendicular bisectors of the sides of APQR meet at the circumcenter V.

Since UV = 48, PS = 62, and RV = 80, we can use these lengths to find the other sides.

The perpendicular bisector UV splits the side AP into PU and UA, and since UV is perpendicular to AP, PU = UA. Similarly, PS is split into PR and RS, and RV is split into RV and BV.

Since the perpendicular bisector TV also passes through V, TV splits the side RP into PR and RV. We can set up the following equations:

PU + UA = 48
PR + RS = 62
RQ + VQ = 80

We can solve this system of equations to find PU = 24, PR = 31, and QV = 49.