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First 2014 puzzle. Dissection of a triangle
Posted 01 January 2014 - 06:00 AM
From P, draw lines to the vertices and perpendiculars to the sides.
Six smaller triangles now touch at P.
Prove that the sums of areas of the two alternating sets of three triangles are equal.
Edited by bonanova, 01 January 2014 - 11:16 PM.
Vidi vici veni.
Posted 01 January 2014 - 04:23 PM
Posted 01 January 2014 - 10:57 PM
Do you mean equilateral instead of isosceles?Spoiler for counterexample for isosceles
Quite right. Equilateral. I changed the OP.
Vidi vici veni.
Posted 22 June 2014 - 04:55 PM
Drat. I just looked over that again and saw that I divided instead of multiplying when manipulating that equation after introducing the deltaA term, so it won't work.
Posted 22 June 2014 - 10:09 PM
Edit: added the figure back
Edited by plasmid, 23 June 2014 - 03:05 PM.
Posted 24 June 2014 - 07:13 AM
(Especially compared to all that slogging I was doing. )
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