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Question

Find the centre and radius of the circle which is inscribed in the triangle formed by the straight lines whose equations are:
y=0, 12x5y=0, and 3x+4y7=0.

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Solution


y=0..................(i)12x5y=0............(ii)3x+4y7=0.............(iii)

Solving (ii) and (iii) we get A(59,43)

Solving (iii) and (i) we get B(73,0)

solving (i) and (ii) we get C(0,0)

BC=a=(730)2+(00)2=73CA=b=(590)2+(430)2=139AB=c=(5973)2+(430)2=209

Coordinates of centre are

⎢ ⎢ ⎢⎪ ⎪ ⎪⎪ ⎪ ⎪73×59+139×73+209×073+139+209⎪ ⎪ ⎪⎪ ⎪ ⎪,⎪ ⎪ ⎪⎪ ⎪ ⎪73×43+139×0+209×073+139+209⎪ ⎪ ⎪⎪ ⎪ ⎪⎥ ⎥ ⎥(79,1427)

Radius is equal to distance from y=0

r=1427



698437_640670_ans_d1cfb0a53e0044f18caf51069d4a3ab0.png

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