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Triangle bounded by rectangles (Posted on 2024-12-11) Difficulty: 2 of 5
There are two rectangles 1 × 2 and 3 × 4 with parallel sides centered at a common point O. Points F and G are selected on the boundary of the inner and outer rectangle, respectively. What is the maximum possible area of triangle FOG?

No Solution Yet Submitted by Danish Ahmed Khan    
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Question re: Solution | Comment 2 of 4 |
(In reply to Solution by Jer)

I'm not clear on what three points you are choosing for the triangles.

Consider just the second case where 1 and 4 are parallel:
Say the center of each rectangle is at (0,0) each rectangle has one vertex in each quadrant.
In Quadrant I, the inner rectangle's vertex is (1/2, 1) and the outer triangle's is (2, 1.5).
One of the triangle's vertices has to be at (0,0), the "O" in "triangle FOG".  The area of the large rectangle is 12; I'm not seeing how any triangle with (0,0) as one of its vertices can have an area as large as 6.

  Posted by Larry on 2024-12-12 08:37:16
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