A circle and a point A are given on the plane. Find the set of midpoints of the segments AN
| August 15, 2021 | education
A circle and a point A are given on the plane. Find the set of midpoints of the segments AN, where N is an arbitrary point of the given circle.
Let us recall the concept of homothety.
Homotetia is a transformation that increases (decreases) a given figure several times.
A more mathematical formulation is as follows: a figure F, a nonzero number k and a point O are selected; then, for each point A of figure F, another point A1 is constructed, such that OA1 = OA * k, where OA1 and OA are vectors.
The figure formed among all points A1 is called the image of the figure F under homothety.
Then, by the condition of the problem, the figure that is obtained at the end is the image of a circle under homothety.
But the image of a circle is a circle.
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