Line Segment That Subtends Equal Angles at Two Other Points
Let, ABC be...
Question
Let, ABC be an isosceles triangle with AB=AC and let Γ denote its circumcircle. A point D is on arc AB of Γ not containing C. A point E is on arc AC of Γ not containing B. If AD=CE, prove that BE is parallel to AD.
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Solution
We note that triangle AEC and triangle BDA are congruent. ∴AE=BD And hence ∠ABE = ∠DAB. This proves that AD is parallel to BE.