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TT2008 Junior A-Level - P6

Source:

September 4, 2010
symmetrygeometryperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be a non-isosceles triangle. Two isosceles triangles AB′CAB'C with base ACAC and CA′BCA'B with base BCBC are constructed outside of triangle ABCABC. Both triangles have the same base angle φ\varphi. Let C1C_1 be a point of intersection of the perpendicular from CC to A′B′A'B' and the perpendicular bisector of the segment ABAB. Determine the value of ∠AC1B.\angle AC_1B.
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