Inscribe a circle in a square

Geometry Level 4

Using a collapsible compass and a straightedge, how many moves are required to construct the inscribed circle of a given square, i.e. a circle tangent to all four sides of a square?

The square has already been drawn for you.

Please refer to the terminology in this note for further definitions. See other problems in this set .

6 5 3 4 7

1 solution

Sharky Kesa
Nov 24, 2016

Let the square be $ABCD$ . Listed beside each instruction is the total number of moves so far.

Draw line $AC$ , a diagonal of the square. (1 move)
Draw a circle centred at $C$ passing through $D$ . (2 moves)
Draw a circle centred at $D$ passing through $C$ . (3 moves)
Let these two circles intersect each other at $E$ and $F$ . (3 moves)
Draw $EF$ . (4 moves)
Let $EF$ intersect $AC$ at $O$ . Let $EF$ intersect $CD$ at $P$ . (4 moves)
Draw a circle centred at $O$ passing through $P$ . (5 moves)

This circle is tangent to all 4 sides of the square, so is the inscribed square we are looking for. This took us 5 moves.

Inscribe a circle in a square

1 solution

0 pending reports