Question 1109797: ABCD is a square A being the bottom left corner and B being the bottom right corner C being the top right corner and D being the top left corner. Points P and Q lie within the square such that AP, PQ and QC are all the same length and AP is parallel to QC. Determine the minimum Possible size of angle DAP. I'm very stuck here so a well explained answer would be highly appreciated :)
Answer by greenestamps(13200)   (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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