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 Misshapen Butter Pats (Posted on 2005-08-16)
While buttering my bread at lunch one day I mused that one can not only cut a square pat of butter in half with only a knife, but also if the pat is in the shape of a regular n-gon, n>3. But what if the pat is shaped like an irregular quadrilateral?

Can you bisect the area of an arbitrary quadrilateral with one straight line using only a straightedge and a compass?

 See The Solution Submitted by McWorter No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 3 of 9 |
` `
`Label the quadrilateral ABCD and construct line AC.Construct a line through B perpendicular to AC andintersecting AC at B'. Construct a line through Dperpendicular to AC and intersecting AC at D'.WOLOG let |BB'| >= |DD'|. Construct point G on linesegment BB' such that`
`  |BG|^2 = (|BB'| + |DD'|)(|BB'|/2).`
`The line through G and parallel to AC is the desired cut.`
` `
` Note: If the quadrilateral is not convex,`
`label so that C is the vertex with interior`
`angle greater than 180 degrees.`

Edited on August 16, 2005, 4:07 pm
 Posted by Bractals on 2005-08-16 15:59:37

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