SOLUTION: ABCD is a square. Points P and Q lie within the square such that AP,PQ and QC are all the same lengths and AP ia parallel to QC. Determine the minimum possible size of angle DAP. Q

Question 1109803: ABCD is a square. Points P and Q lie within the square such that AP,PQ and QC are all the same lengths and AP ia parallel to QC. Determine the minimum possible size of angle DAP. Question number S3 answer
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Draw a few examples which satisfy the given conditions.

Start with P and Q being on diagonal AC so that angle DAP is 45 degrees. Then move P and Q left and right (or vice versa) maintaining the requirements of the problem.

You should see that the limiting case (the longest possible length of AP, PQ, and QC) is when P is on CD with DP:PC = 1:2 and Q is on AB with AQ:QB = 2:1. In that case, the size of the angle is arctan(1/3).

If P and Q must be INSIDE the square, then there is no answer to the question, because the angle can get as close as you want to arctan(1/3) without getting there.
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