A cyclic quadrilateral has side lengths a, c, j, and k. Three segments drop perpendicularly to two sides and one diagonal of the quad, forming the green and purple triangles between them. What is the ratio purple/green, in terms of a, c, j, k?
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Solution
Purple/green=ck/aj.
BD/DE=BD/DF×DF/DE
purple/green=c/j×k/a=(ck)/(aj)
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