# Difference between revisions of "2020 IMO Problems/Problem 1"

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− | Problem 1. Consider the convex quadrilateral ABCD. The point P is in the interior of ABCD. | + | <math>\textbf{Problem 1}</math>. Consider the convex quadrilateral <math>ABCD</math>. The point <math>P</math> is in the interior of <math>ABCD</math>. The following ratio equalities hold: |

− | The following ratio equalities hold: | + | <cmath>\angle PAD : \angle PBA : \angle DPA = 1 : 2 : 3 = \angle CBP : \angle BAP : \angle BPC</cmath> |

− | + | Prove that the following three lines meet in a point: the internal bisectors of angles <math>\angle ADP</math> and | |

− | Prove that the following three lines meet in a point: the internal bisectors of angles | + | <math>\angle PCB</math> and the perpendicular bisector of segment <math>AB</math>. |

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== Video solution == | == Video solution == | ||

## Revision as of 16:33, 8 October 2020

. Consider the convex quadrilateral . The point is in the interior of . The following ratio equalities hold: Prove that the following three lines meet in a point: the internal bisectors of angles and and the perpendicular bisector of segment .

## Video solution

https://youtu.be/bDHtM1wijbY [Shorter solution, video covers all day 1 problems]