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Cyclic Quadrilateral Circles | Wizako - GRE Prep Blog
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Cyclic Quadrilateral Circles

K S Baskar
In a cyclic quadrilateral ABCD, the diagonals intersect at E. If AE = 4 and EC = 9, what is the minimum length of diagonal BD?
Answer: 12

Explanation

We know that when two chords of a circle intersect at a point,
AE*EC = BE*ED
Hence, BE*ED = 4*9 = 36.
Given the product of two quantities their sum is minimum when the two quantities are equal. Hence when BE = ED = 6 BE+ED is minimum.
Hence, the minimum length of diagonal BD is 12.

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