MathDB
Turkey NMO 2000 1st Round - P33 (Geometry)

Source:

July 25, 2012
geometrytrigonometryquadraticsPythagorean Theoremangle bisector

Problem Statement

Let KK be a point on the side [AB][AB], and LL be a point on the side [BC][BC] of the square ABCDABCD. If ∣AK∣=3|AK|=3, ∣KB∣=2|KB|=2, and the distance of KK to the line DLDL is 33, what is ∣BL∣:∣LC∣|BL|:|LC|?
<spanclass=′latex−bold′>(A)</span> 78<spanclass=′latex−bold′>(B)</span> 32<spanclass=′latex−bold′>(C)</span> 87<spanclass=′latex−bold′>(D)</span> 38<spanclass=′latex−bold′>(E)</span> 22 <span class='latex-bold'>(A)</span>\ \frac78 \qquad<span class='latex-bold'>(B)</span>\ \frac{\sqrt 3}2 \qquad<span class='latex-bold'>(C)</span>\ \frac 87 \qquad<span class='latex-bold'>(D)</span>\ \frac 38 \qquad<span class='latex-bold'>(E)</span>\ \frac{\sqrt 2}2
Back to ProblemsView on AoPS