Q. 93.5( 60 Votes )

In the figure 2.22, M is themidpoint of QR. PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2


Answer :

In ∆PRQ, PRQ = 900


PQ2 = PR2 + QR2 – – – 1


In ∆PRM, PRM = 900


PM2 = PR2 + MR2


PM2 = PR2 + 2 [ M is midpoint]


4(PM2 – PR2) = QR2 – – – 2


1 And 2 implies


PQ2 = PR2 + 4(PM2 – PR2)


PQ2 = 4PM2 – 3PR2


PROVED.


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