I'm designing something that involves a folding A-frame in the form of a triangle, hinged at each corner. Two of the sides are rigid, but the third is divided by a hinged joint.

If the 2 rigid sides are of equal length, and the hinge on the 3rd side is in the middle, then the whole frame can be folded flat. The problem comes when the two rigid sides are of unequal length - how to place the hinge so that it still folds flat?

In the following schematic, **A**,**B **and **C **are the hinges at the corners, and **D **is the hinge on the 3rd side. The top diagram shows how 2 equal sides and a centre joint folds flat. The other 2 diagrams show what happens when the 2 rigid sides are unequal. The centre diagram shows the result of placing the hinge on the altitude bisector - this clearly doesn't fold flat.

The bottom diagram shows the hinge placed so that the difference in lengths between the hinge arms is equal to the difference in lengths of the 2 rigid sides. This folds flat nicely, but the position of the hinge has either to be calculated and measured (very tedious), or determined by rather a lot of auxiliary drawing construction involving circles.

Is there an easy way to draw it?

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Gary Wooding

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