Inscribe a rhombus inside a rectangle
Using a collapsible compass and a straightedge, how many moves are required to construct the inscribed rhombus of a given rectangle?
The rectangle is not a square and has already been drawn for you.
Please refer to the terminology in this note for further definitions. See other problems in this set .
The answer is 5.
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1 solution
Let the rectangle be A B C D with A B > B C . Listed beside each instruction is the total number of moves so far.
Draw a circle centred at B passing through D . (1 move)
Draw a circle centred at D passing through B . (2 moves)
Let these two circles intersect each other at E and F . (2 moves)
Draw line E F . (3 moves)
Let E F intersect A B and C D at P and Q respectively. (3 moves)
Draw B Q and D P . (5 moves)
Hence, B Q D P is a rhombus, and this took 5 moves.