Perpendicular Chords in a Circle


Let X be a fixed point within a given circle. Let A, B, C and D be variable points on the circle such that AC and BD are perpendicular chords through X. For each X, find the maximum and minimum of (a) the area of the quadrilateral ABCD, and (b) the sum of the lengths of AC and BD.


To see a GSP sketch for this construction, click here.


Solution and discussion.


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