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Question

The vertices of the triangles ABC are the points (6 , 0) ,( 0 , 6 ) and (7 , 7 ) prove that the equation of the circle inscribe in the triangle is
x2+y2 9x - 9y + 36 = 0

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Solution

Centre is obtained by using the formula (ax1a,ay1a) for incentre
(722162,722162) or (92,92)
Radius is distance of centre from any side say AB whose equation by intercepts from is
xy+yx = 1 or x + y - 6 = 0
r=92+9262=32
Circle is
(x92)2+(y92)2=(32)2
or x2+y2 - 9x - 9y + 36 = 0

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