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- x1, y1, x2, y2 = var('x1, y1, x2, y2') # tangent points
- m1, b1, m2, b2 = var('m1, b1, m2, b2') # lines' eqn
- x0, y0, r = var('x0, y0, r') # cirsle's eqn
- eq1 = (x1 - x0)^2 + (y1 - y0)^2 - r^2 == 0
- eq2 = (x2 - x0)^2 + (y2 - y0)^2 - r^2 == 0
- eq3 = y1 - m1*x1 - b1 == 0
- eq4 = y2 - m2*x2 - b2 == 0
- eq5 = (y1-y0)/(x1-x0) == -1/m1
- eq6 = (y2-y0)/(x2-x0) == -1/m2
- # unknown: x0,y0,x1,y1,x2,y2
- # known: m1,b1,m2,b2,r
- solve([eq1,eq2,eq3,eq4,eq5,eq6,
- x1>0,y1>0,x2>0,y2>0,
- m1<=0,b1>=0,m2<m1,b2>b1,
- x0>x2,y0>y1,r>0],x0,y0,x1,y1,x2,y2)
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