Wednesday, January 19, 2011

Problem 569: Quadrilateral, Excircles, Tangency Points, Congruence

Geometry Problem
Click the figure below to see the complete problem 569.

Problem 569: Quadrilateral, Excircles, Tangency Points, Congruence.
Zoom at: Geometry Problem 569

Posted by Antonio Gutierrez at 9:10 AM
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2 comments:

  1. c .t . e. oJanuary 19, 2011 at 9:51 AM

    ▲ERL, ▲GPJ, ▲LQJ, ▲ENG isoceles ( REL=RLE,90-EAF... )
    EN + NR = LQ + QR, JQ + PQ = GN + PN, LQ = JQ, GN = EN
    => NR + PQ = NP + RQ

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  2. Peter TranJanuary 19, 2011 at 12:01 PM

    Connect G,B, E and note that G, B, E are collinear and EN= GN ( see problem 568)
    Similarly G,C,J are collinear and PG=PJ . J,D,L are collinear and QJ=QL . E,A,L are collinear and RE=RL

    We have NP=PG-NG
    RQ=RL-QL
    And NP+RQ= PG-NG+RL-QL
    Replace PG by PJ , NG by NE , RL by RE and QL by QJ we get
    NP+RQ= PJ-NE+RE-QJ = PQ+NR

    Peter Tran

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