Intersection of two chords

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Let AB and CD be two intersecting chords of a circle. How can I find the coordinates of the intersection point knowing only the euclidean coordinates of the endpoints A,B,C,D and the circle center point?

This can of course be solved with a segment-segment intersection algorithm (thanks for marking this question as duplicate, everyone), but I am asking if there is a simpler or more efficient algorithm that exploits the fact that the two line segments are chords of the same circle.