MathDB
2018 JHMT Geometry #7

Source:

September 5, 2023
geometry

Problem Statement

Let ℓ1\ell_1, ℓ2\ell_2, ℓ3\ell_3m ℓ4\ell_4 be rays from the origin, intersecting the line y=1y = 1 at xx-coordinates −8-8,−2-2, 11, 22, respectively. For −18<k<12-\frac18 < k < \frac12 , the line y=1+kxy = 1 + kx intersects the four rays at points A,B,C,DA,B,C,D, respectively. When AB‾=CD‾\overline{AB} = \overline{CD}, the ratio AB‾BC‾\frac{\overline{AB}}{\overline{BC}} is pq\frac{p}{q} where p,qp, q are relatively prime positive integers. Find p+qp + q.
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