A geometry problem by Shivam Jadhav

Geometry Level 3

If the equation of a circle with the centre on the line \[ 2x+y=0 \] and touching the lines \[4x-3y-30=0 , 4x-3y+10=0\] can be represented by \[(x-a)^{2} + (y+b)^{2} = m^{2}\] then find the value of \[m^{0.5} + a +b\].

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