Friday, March 10, 2017

Geometry Problem 1321: Intersecting Circles, Diameter, Secant, Chord, Collinearity

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1321: Intersecting Circles, Diameter, Secant, Chord, Collinearity.

Posted by Antonio Gutierrez at 12:25 PM
Labels: , , , , ,

2 comments:

  1. Peter TranMarch 10, 2017 at 1:11 PM

    Since AB and CD are diameters of circles O and Q
    So angle AGD= AKD= 90 => AGKD is cyclic
    LA.LK=LD.LG=> power of L is the same to both circles O and Q
    So L is on radical line EF.
    Similarly for point M

    ReplyDelete
  2. APOSTOLIS MANOLOUDISMarch 10, 2017 at 1:47 PM

    Problem 1321
    EF is the radical axis of the circles O, Q. Is AB diameter then BH perpendicular in AC and BK perpendicular in AK similar DG, CJ are perpendiculars in AC ,BD respectively .Is <BHC=90=<BJC so BJHC is cyclic or JM.MC=BM.MH. But JM.ME is the power of point M with respect to the circle with center Q and BM.MH is the power of point M with respect to the circle with center O.Therefore the point M belongs to the radical axis EF.Similar
    The point L belongs to the radical axis EF (<AGD=90=<AKD and AGKD is cyclic GL.LD=
    AL.LK).
    APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE

    ReplyDelete

Subscribe to: Post Comments (Atom)