Circle Inscribing a Triangle Formed by 3 Given Lines

Q. The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

1. $6(x^2+y^2)-5(3x+2y)=0$
2. $x^2+y^2+2x+3y-5=0$
3. $x^2+y^2-2x-3y+5=0$
4. $6(x^2+y^2)+5(3x+2y)=0$

Q.

Find the equation of the circle circumscribing the triangle formed by the lines $x+y=0,2x+y=4$ and $x+2y=5$

1. x² + y² + 17x + 19y + 50 = 0

2. x² + y² - 17x - 19y + 50 = 0

3. x² + y² + 17x - 11y + 30 = 0

4. x² + y² - 17x - 11y + 30 = 0

Q.

Find the equation of the circle circumscribing the triangle formed by the lines $L_1=0,L_2=0$and $L_3=0$

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Q. Tangents are drawn from any point on the circle $x^2+y^2=R^2$ to the circle $x^2+y^2=r^2$. If the line joining the points of intersection of these tangents with the first circle also touch the second, then R equals

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