Proof:
In ∆PMR,
QM = QR = a ---- [Given]
\(\therefore\) Q is midpoint of seg MR.
\(\therefore\) seg PQ is the median
\(\therefore\) PM2 + PR2 = 2PQ2 + 2QM2 ---- [By Apollonius theorem]
\(\therefore\) PM2 + a2 = 2a2 + 2a2 ---- [Substituting the given values]
\(\therefore\) PM2 + a2 = 4a2
\(\therefore\) PM2 = 4a2 - a2
\(\therefore\) PM2 = 3a2
\(\therefore\) PM = √3 a ---- [Taking square root on both sides]
Similarly, we can prove
PN = √3 a
\(\therefore\) PM = PN = √3 a
