Question

PQR is an isosceles triangle,PQ=QR. RQ is produced to M. PM is perpendicular to QR. Prove that PR^2=2QR*MR​

Answer 1

Brainly.in

What is your question?

1

Secondary School Math 5 points

PQR is a triangle in which QM perpendicular to PR and PR square - PQ square = QR square. Prove that QM square = PM*MR

Ask for details Follow Report by Ajayhudge9048 28.12.2017

Answers

Geekydude121

Geekydude121 Virtuoso

Given that

PQR is a triangle and QM is perpendicular on PR

Also,

PR^2 - PQ^2 = QR^2

Now in traingle QMR

QR^2 = QM^2+MR^2

Thus fro above two equations for QR

We get

PR^2 - PQ^2 = QM^2 + MR^2

QM^2 = PR^2 - PQ^2 -MR^2

QM^2 = (PM+MR)^2 - PQ^2 - MR^2

QM^2 = PM^2 + MR^2 + 2PM*MR - PQ^2 - MR^2

QM^2 = PM^2 + 2 PM^MR - PQ^2

QM^2 = PQ^2 - QM^2 + 2PM*MR - PQ^2

thus, 2QM^2 = 2 PM * MR

Hence prooved

DO IT IN THE SAME WAY