Through one of the two intersection points of two circles, a diameter in each of the circles is drawn. Prove that the line connecting the endpoints of these diameters passes through the other intersection point.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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The problem comes from the textbook, Kiselev's Geometry. Book I. Planimetry by A. P. Kiselev:

  1. Prove theorem: Through one of the two intersection points of two circles, a diameter in each of the circles is drawn. Prove that the line connecting the endpoints of these diameters passes through the other intersection point.
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