SOLUTION: Lines l, m, and n are perpendicular bisectors of triangle PQR and meet at T. If TQ=2x, PT=3y-1, and TR=8, find x, y, and z.

Algebra ->  Points-lines-and-rays -> SOLUTION: Lines l, m, and n are perpendicular bisectors of triangle PQR and meet at T. If TQ=2x, PT=3y-1, and TR=8, find x, y, and z.      Log On


   

Question 1022458: Lines l, m, and n are perpendicular bisectors of triangle PQR and meet at T. If TQ=2x, PT=3y-1, and TR=8, find x, y, and z.
Answer by ikleyn(52847) About Me  (Show Source):
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Lines l, m, and n are perpendicular bisectors highlight%28of_the_sides_of_a%29 triangle PQR and meet at T.
If TQ=2x, PT=3y-1, and TR=8, find x, y, and z.
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For any triangle, the perpendicular bisectors of its sides  are concurrent.
It means they intersect in one point.
   (see the lesson Perpendicular bisectors of a triangle sides are concurrent in this site).

This intersection point is the center of the circle which is circumscribed circle of the triangle.

It means that the vertices of the triangle are equidistant from that intersection point.

Regarding your problem, it means that the lengths of the segments TQ, PT and TR are the same.

Hence,

2x = 3y-1 = 8.

Then x = 4 and y = 3.

The "z" you are asking for, is not a part of the problem.