Question

PQR is a right angled triangle right angled at Q. S is a point on QR such that QS=SR,show that PR 2 = 4PS 2 3PQ 2

Answer 1

In the right angle ΔPQR, S is the midpoint of QR.
So      QR² = PR² - PQ²  and   also

ΔPQS is right angled at Q.  
 So  PS² = PQ² + QS²
              = PQ² + QR²/4
              = PQ²  + (PR² - PQ²) / 4
              = 3/4 * PQ² + PR² / 4                   

So PR² = 4 PS² - 3 PQ²

Answer 2

here is your answer.... .