Show that a cyclic quadrilateral is formed by the lines $5x+3y=9$, $x=3y$, $2x=y$ and $x+4y+2=0$ taken in order. Find the equation of the circumscribing circle. How do i go about it?
2026-04-25 14:41:30.1777128090
Equation of circumscribing circle
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Hint: We can compute. Find the vertices by solving the appropriate systems of two linear equations in two unknowns.
The perpendicular bisectors of two consecutive edges meet at the centre of the circle. One of the vertices is the origin, so the arithmetic will be relatively pleasant.
Once you have used three vertices to find the equation of the circle, you can check whether the quadrilateral is cyclic by seeing whether the circle goes through the fourth vertex.