Difference between revisions of "1998 IMO Problems/Problem 1"
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In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular | In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular | ||
and the opposite sides AB and DC are not parallel. Suppose that the point P , | and the opposite sides AB and DC are not parallel. Suppose that the point P , | ||
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that ABCD is a cyclic quadrilateral if and only if the triangles ABP and CDP | that ABCD is a cyclic quadrilateral if and only if the triangles ABP and CDP | ||
have equal areas. | have equal areas. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
Revision as of 22:45, 18 November 2023
Problem
In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular and the opposite sides AB and DC are not parallel. Suppose that the point P , where the perpendicular bisectors of AB and DC meet, is inside ABCD. Prove that ABCD is a cyclic quadrilateral if and only if the triangles ABP and CDP have equal areas.
Solution
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