Question #94a03

1 Answer
Zor Shekhtman
Mar 22, 2016

Use two pairs of points: P on original with its rotated image P' and Q on original with its rotated image Q'.
Perpendiculars to PP' and Q Q' at their midpoints go through center.

Explanation:

Let P and Q are two points on an original figure. The corresponding points on a rotated figure are P' and Q'.

As we know, a perpendicular to a midpoint of a chord is a diameter of a circle of rotation. Therefore, a perpendicular to a midpoint of PP' is a diameter.
So is a perpendicular to a midpoint of Q Q'.

Thus, having two diameters, we get a center O.

The angle of rotation is /_POP'.

Related questions
See all questions in Circumference and Area of Circles
Impact of this question
1910 views around the world
You can reuse this answer
Creative Commons License