Question

Can you find if the points of intersection of all the perpendicular bisectors for an obtuse triangle PQR with measurements as follows: PQ = 5 units, QR = 8 units, and PR = 9 units lies outside or inside the triangle?

Answer 1

The perpendicular bisector of any triangle bisects the sides at its midpoint. In a triangle, there are three perpendicular bisectors that can be drawn from each side. To find the perpendicular bisector of a triangle with the given sides, follow the steps given below.
1.Draw a line segment PQ of length 5 units.
2.With P as the center and more than half of PQ as radius, draw arcs above and below the line segment PQ. Repeat the same process with Q as the center. Join the points of intersection of these arcs.
3.Repeat the same process and draw perpendicular bisectors for the sides QR and PR. The construction of the perpendicular bisectors of the obtuse triangle is shown below.
We can clearly see that all the perpendicular bisectors bisect at a point outside the triangle.