Question

A circle is inscribed in a triangle PQR touching PQ, QR, PR at X,Y,Z respectively.
If PQ = 10 cm, PZ = 7 cm and RZ = 5 cm, find the length of QR.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:Since lenth from an exterior point to a circle are equal.

Therefore PX=PZ.....1

                QY=QX......2

                RZ=RY........3

Adding equation 1,2 and 3 ,we get

PX+QY+RZ = PZ+QX+RY

Now,

      Perimeter of triangle PQR =PQ+PR+QR

= (PX+XQ)+(QY+YR)+(PZ+ZR)

= (PX+PZ)+(QX+QY)+(RZ+RY)

= 2PX+2QY+2RZ

= 2(PX+QY+RZ)

Therefore,PX+QY+RZ = XQ+YR+ZP =  1/2

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(perimeter of triangle PQR)

hope it helps u