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1

Part of 2001 Mediterranean Mathematics Olympiad

Problems(1)

the intersection point depends only on k and P, Q

Source: Mediterranean MO 2001

10/31/2010
Let PP and QQ be points on a circle kk. A chord ACAC of kk passes through the midpoint MM of PQPQ. Consider a trapezoid ABCDABCD inscribed in kk with AB∥PQ∥CDAB \parallel PQ \parallel CD. Prove that the intersection point XX of ADAD and BCBC depends only on kk and P,Q.P,Q.
geometrytrapezoidsymmetryparallelogramrectangleperpendicular bisectorgeometry unsolved