Problem: 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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