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Question

A triangle PQR is drawn to circumsribe a circle of radius 8 cm such that the segements QT and TR, into which QR is divided by the point of contact T, are of lengths 14 cm and 16 cm respectively. If area of ΔPQR is 336cm2, find the sides PQ and PR.


Solution

Since length of tangents drawn from a point to a circle are equal.

  QS= AT = 14cm, RU =RT =16cm and, PS = PU = x.

Thus, PQ=x+14, PR =x+16 and QR =30


Now, Area of ΔPQR = Area of ΔIQR + Area of ΔIPR


 336=12(QR×8)+12(14+2)×8+12(16+x)×8

 84=30+14+x+16+x

 24=2x x=12

Hence, PQ=26 cm and PR =28 cm


Mathematics
RD Sharma
Standard X

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