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Consider a circle (C) of center O and a line (d) exterior to (C). Through a point M on (d) we draw the tangents (MA) and (MB) to (C). A and B are points on (C). E is the orthogonal projection of O on (d). Prove that A, O, B, E and M belong to the same circle of diameter to be determined.

Consider a circle (C) of center O and a line (d) exterior to (C). Through a point M on (d) we draw the tangents (MA) and (MB) to (C). A and B are points on (C). E is the orthogonal projection of O on (d). Prove that A, O, B, E and M belong to the same circle of diameter to be determined.

Elementary Geometry For College Students, 7e
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
Problem 1CT
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Consider a circle (C) of center O and a line (d) exterior to (C). Through a point M on (d) we draw the tangents (MA) and (MB) to (C). A and B are points on (C). E is the orthogonal projection of O on (d). Prove that A, O, B, E and M belong to the same circle of diameter to be determined.
Transcribed Image Text:Consider a circle (C) of center O and a line (d) exterior to (C). Through a point M on (d) we draw the tangents (MA) and (MB) to (C). A and B are points on (C). E is the orthogonal projection of O on (d). Prove that A, O, B, E and M belong to the same circle of diameter to be determined.
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