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The Cross in the Trapezoid (Posted on 2007-03-03) Difficulty: 2 of 5
Consider trapezoid ABCD where BC is perpendicular to AB and CD. Consider also that the diagonals AC and BD are perpendicular to each other and intersect at point E.

If EA = 6.25 and ED = 3.2, then what are EB and EC?

No Solution Yet Submitted by hoodat    
Rating: 2.0000 (3 votes)

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Solution Cross multiplying (spoiler) | Comment 1 of 3
Triangles ABE, BEC, and CED are all similar to each other.

3.2/CE = CE/EB = EB/6.25

So, ED, EC, EB, EA form a geometric progression.

3.2/6.25 = 64/125 = (4/5)^3, so each term is 4/5 of the next.

ED, EC, EB, EA are 3.2, 4, 5, 6.25 respectively

  Posted by Steve Herman on 2007-03-03 09:04:42
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