Problem
GEO-B2-M09-P016 An Isosceles Trapezoid Is Cyclic
#16
★★★☆☆ Level 3 of 5
Prove that points \(A(-3,0)\), \(B(3,0)\), \(C(2,2)\), \(D(-2,2)\) lie on one circle.
Try a circle with centre on the \(Oy\)-axis: \(x^2+(y-k)^2=R^2\).
By symmetry the centre should lie on the \(Oy\)-axis. Check the circle \(x^2+\left(y+\frac14\right)^2=\frac{145}{16}\). For \(A\) and \(B\): \(9+\frac{1}{16}=\frac{145}{16}\). For \(C\) and \(D\): \(4+\frac{81}{16}=\frac{145}{16}\). All four points satisfy one circle equation.
A good example of a coordinate proof of concyclicity.