a tangent pr touches a circle at point p and pq is diameter of cir cle =8 pr-=6 cm qr cut the circle at point m then find the ratio of triangle perimeter pmr to pqr

• PR^2 = RM*RQ
  =>RM*RQ = 6^2 = 36 ....1.
  also,
  in right-angled triangle
  PR^2 + PQ^2 = QR^2
  => 36 + 64 = QR^2
  =>QR = 10 ....2.
  using 1. and 2. we get
  MR = 3.6
  so, QM = QR - MR = 10-3.6 = 6.4
  now, since PQ is a diameter
  som PMQ is a right-angled triangle right angled at M
  so, PM = sqrt(PQ^2 - QM^2) = sqrt(10^2 - 6.4^2) = 4.8
  perimeter of PMR = PM + MR + PR = 6+3.6+4.8 = 14.4
  perimeter of PQR = PR + QR + PQ = 8 + 6+ 10 = 28
  so ratio = 14.4/28 = 18/35
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