MathDB
2007 Guts #36: The Marathon

Source:

June 22, 2012
geometryfloor function

Problem Statement

The Marathon. Let ω\omega denote the incircle of triangle ABCABC. The segments BCBC, CACA, and ABAB are tangent to ω\omega at DD, EE and FF, respectively. Point PP lies on EFEF such that segment PDPD is perpendicular to BCBC. The line APAP intersects BCBC at QQ. The circles ω1\omega_1 and ω2\omega_2 pass through BB and CC, respectively, and are tangent to AQAQ at QQ; the former meets ABAB again at XX, and the latter meets ACAC again at YY. The line XYXY intersects BCBC at ZZ. Given that AB=15AB=15, BC=14BC=14, and CA=13CA=13, find ⌊XZ⋅YZ⌋\lfloor XZ\cdot YZ\rfloor.
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