Two circles with centers O1 and O2 meet at points A and B. Prove that the segments AB
| May 9, 2021 | education
Two circles with centers O1 and O2 meet at points A and B. Prove that the segments AB and O1O2 are perpendicular.
In order to prove that the segments AB and O1O2 are perpendicular, let’s go from the opposite. Let’s assume that AB and O1O2 are not perpendicular to each other.
If AB and O1O2 are not perpendicular, then the segments AO1 and BO1 are not equal.
However, this statement is incorrect, since AO1 and BO1 are the radii of a circle centered at O1.
Thus, we can conclude that AB and O1O2 are perpendicular to each other.
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