MathDB
2015-2016 Fall OMO #11

Source:

November 18, 2015
Online Math Open

Problem Statement

A trapezoid ABCDABCD lies on the xyxy-plane. The slopes of lines BCBC and ADAD are both 13\frac 13, and the slope of line ABAB is −23-\frac 23. Given that AB=CDAB=CD and BC<ADBC< AD, the absolute value of the slope of line CDCD can be expressed as mn\frac mn, where m,nm,n are two relatively prime positive integers. Find 100m+n100m+n.
Proposed by Yannick Yao
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