Centre of a circle

Geometry Level 4

Using a collapsible compass and a straightedge, how many moves are required to construct the centre of a given circle?

The circle has no marked points on it, just a circumference.

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

7 5 4 6 3

1 solution

Sharky Kesa
Nov 24, 2016

From an arbitrary point $A$ on the circumference of the circle, draw a circle with a small radius. (1 move)
Let these two circles intersect at $B$ and $C$ . (2 moves)
Draw circles centred at $B$ and $C$ , both passing through $A$ . (3 moves)
Let the circle centred at $B$ intersect the circle centred at $A$ at points $D$ and $E$ . Similarly, let the circle centred at $C$ intersect the circle centred at $A$ at points $F$ and $G$ . (3 moves)
Draw $DE$ and $FG$ . (5 moves)
Let the two lines intersect at $O$ .

$O$ is the centre of the circle, and it took 5 moves.