(-6,0), (0, 6), and (-7,7) are the vertices of a $∆$ABC .The incircle of the triangle has equation 

detailed solution

Correct option is B

The Triangle is evidently isosceles and , therefore ,the median through C is the angle bisector of ∠CThe equation of the angle bisector is y = -X and the incenterI ≡(-a, a), where a is Positive'The equation of AC is y-0 =-7(x+6), 7x+3y+42=0and the equation of AB is x-y+6=0The perpendiculars From I to AB and AC are equal. therefore,−7a+a+4250=−a−a+62a=92 (∵a>0)Therefore the centre is (−9/2,9/2) and the radius is 32Hence, the equation of the circle isx+922+y−922=92or x2+y2+9x−9y+36=0