From Archimedes Book of Lemmas: Proposition 13. Given a circle with center O and diameter AB. Let AD intersect a chord CD, which is not the diameter of the circle. Construct a perpendicular from A to CD that intersects CD at point M. Construct a perpendicular from B to CD that intersects CD at point N. Then CN = DM. Prove this lemma.

From Archimedes Book of Lemmas: Proposition 13. Given a circle with center O and diameter AB. Let AD intersect a chord CD, which is not the diameter of the circle. Construct a perpendicular from A to CD that intersects CD at point M. Construct a perpendicular from B to CD that intersects CD at point N. Then CN = DM. Prove this lemma.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter6: Circles

Section6.3: Line And Segment Relationships In The Circle

Problem 44E: In Exercises 44 to 47, prove the stated theorem. If a line is drawn through the center of a circle...

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