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Consider 4 circles S1, S2, S3, S4. Suppose that S1, S2 intersect at A1 and A2, circles S2, S3 intersect at Bi and B2, circles S3, S4 intersect at Ci and C2, and circles S4, S1 intersect at D1 and D2. Suppose furthermore that the points A1, Prove that the points A2, B2, C2, D2 B1, C1, D1 are on a circle S (or on a line) are also on a circle (or on a line).

Consider 4 circles S1, S2, S3, S4. Suppose that S1, S2 intersect at A1 and A2, circles S2, S3 intersect at Bi and B2, circles S3, S4 intersect at Ci and C2, and circles S4, S1 intersect at D1 and D2. Suppose furthermore that the points A1, Prove that the points A2, B2, C2, D2 B1, C1, D1 are on a circle S (or on a line) are also on a circle (or on a line).

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.
Chapter6: Circles
Section6.4: Some Constructions And Inequalities For The Circle
Problem 11E: X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is...
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Consider 4 circles S1, S2, S3, S4. Suppose that S1, S2 intersect at A1 and A2, circles S2, S3 intersect at Bi and B2, circles S3, S4 intersect at Ci and C2, and circles S4, S1 intersect at D1 and D2. Suppose furthermore that the points A1, Prove that the points A2, B2, C2, D2 B1, C1, D1 are on a circle S (or on a line) are also on a circle (or on a line).
Transcribed Image Text:Consider 4 circles S1, S2, S3, S4. Suppose that S1, S2 intersect at A1 and A2, circles S2, S3 intersect at Bi and B2, circles S3, S4 intersect at Ci and C2, and circles S4, S1 intersect at D1 and D2. Suppose furthermore that the points A1, Prove that the points A2, B2, C2, D2 B1, C1, D1 are on a circle S (or on a line) are also on a circle (or on a line).
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