Question

Question #94a03

Answer 1

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'`.