Tuesday, June 29, 2010

Problem 466: Concentric Circles, Secant, Congruence, Measurement

Geometry Problem
Click the figure below to see the complete problem 466 about Concentric Circles, Secant, Congruence, Measurement.

Problem 466: Concentric Circles, Secant, Congruence, Measurement
See also:
Complete Problem 466

Level: High School, SAT Prep, College geometry


  1. Let point H is the projection of the center O of concentric circles to the secant
    We have HB=HC and HA=HD (property of the secant)

    So AB=CD

    Peter Tran
    Email: vstran@yahoo.com

  2. Let O be the circles' center. Bring AO,BO,CO,DO.
    Then ABO=DCO(BCO isoscles),BAO=CDO(ADO isosceles).
    Thus AOB=DOC so the triangles ABO and CDO are equal( their sides are radius of cirlces) So AB=CD

  3. Let point M be the common center of C1 and C2.
    Let MN be perpendicular to chord BC.
    Hence, MN is perpendicular to chord AD.
    Perpendicular drawn from center of the circle to the chord of the same circle bisects the chord.(1)
    Hence,AN = ND and BN = DN...(by(1))
    AN-BN = DN-CN
    AB = CD.