Question

QT AND RS are the medians of a triangle PQR right angled at p. Prove that (QT^2+RS^2)=5QR^2.

Answer 1

TQ²+RS²= (TP²+PQ²)+(RP²+PS²)

             =(PR²/4)+PQ²+RP²+(PQ²/4)

             =[PR²+4PR²]/4+[4PQ²+PQ²]/5

             =5(PR²+PQ²)/4

              =5QR²/4

4(TQ²+RS²)=5QR²

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Answer 2

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