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Two Squares (Posted on 2009-04-20) Difficulty: 2 of 5
In the diagram below, ABCD and DEFG are congruent squares, and angle CDG is 60°.

What is angle ACF?

  Submitted by Charlie    
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Solution: (Hide)
If point D is taken as the origin, and the sides of the squares are unit length, then point G is at (sqrt(3)/2, -1/2), and point F is at (sqrt(3)/2 + 1/2, sqrt(3)/2 - 1/2), while point C is at (0, -1). This makes line CF have a slope of 1, and at an angle of 45° with CD, adding to the 45° of DCA, making the total angle ACF equal 90°.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Puzzle Thoughts K Sengupta2023-02-13 03:57:59
Solution -- How Geo?brianjn2009-04-27 07:20:38
re(2): SolutionCharlie2009-04-21 11:40:39
re(2): Solutioned bottemiller2009-04-21 10:39:37
re: Solutionbrianjn2009-04-20 22:49:36
Diagram to Scale?ed bottemiller2009-04-20 17:35:07
SolutionRosy2009-04-20 13:47:18
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