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\includegraphics[max width=\textwidth, alt={}, center]{68f1107f-f188-4698-934e-8fd593b25418-4_442_661_840_260}
The diagram shows triangle \(A B C\), with \(A B = x \mathrm {~cm} , A C = y \mathrm {~cm}\) and angle \(B A C = 60 ^ { \circ }\). It is given that the area of the triangle is \(( x + y ) \sqrt { 3 } \mathrm {~cm} ^ { 2 }\).
- Show that \(4 x + 4 y = x y\).
When the vertices of the triangle are placed on the circumference of a circle, \(A C\) is a diameter of the circle.
- Determine the value of \(x\) and the value of \(y\).