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A_1D _|_ B_1C , <A_1B_1C = 1/2<ABC , A_1B_1 // AB, ABCD parallelogram

Source: 1996 Argentina OMA L3 p4

June 11, 2020
perpendiculargeometryparallelogramequal anglesparallel

Problem Statement

Let ABCDABCD be a parallelogram with center OO such that ∠BAD<90o\angle BAD <90^o and ∠AOB>90o\angle AOB> 90^o. Consider points A1A_1 and B1B_1 on the rays OAOA and OBOB respectively, such that A1B1A_1B_1 is parallel to ABAB and ∠A1B1C=12∠ABC\angle A_1B_1C = \frac12 \angle ABC. Prove that A1DA_1D is perpendicular to B1CB_1C.
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