MathDB

2003.G6

Part of Cono Sur Shortlist - geometry

Problems(1)

locus of lines' intersection from Cono Sur, condition 1/TH= 1/d -1/PH

Source: Cono Sur Shortlist 2003 G6

7/26/2019
Let L1L_1 and L2L_2 be two parallel lines and L3L_3 a line perpendicular to L1L_1 and L2L_2 at HH and PP, respectively. Points QQ and RR lie on L1L_1 such that QR=PRQR = PR (Q≠HQ \ne H). Let dd be the diameter of the circle inscribed in the triangle PQRPQR. Point TT lies L2L_2 in the same semiplane as QQ with respect to line L3L_3 such that 1TH=1d−1PH\frac{1}{TH}= \frac{1}{d}- \frac{1}{PH} . Let XX be the intersection point of PQPQ and THTH. Find the locus of the points XX as QQ varies on L1L_1.
geometryLocusParallel Lines