Geometry Problem
Click the figure below to see the complete problem 466 about Concentric Circles, Secant, Congruence, Measurement.
See also:
Complete Problem 466
Level: High School, SAT Prep, College geometry
Tuesday, June 29, 2010
Problem 466: Concentric Circles, Secant, Congruence, Measurement
Subscribe to:
Post Comments (Atom)
Let point H is the projection of the center O of concentric circles to the secant
ReplyDeleteWe have HB=HC and HA=HD (property of the secant)
AB=HA-HB
CD=HD-HC
So AB=CD
Peter Tran
Email: vstran@yahoo.com
Let O be the circles' center. Bring AO,BO,CO,DO.
ReplyDeleteThen 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
Let point M be the common center of C1 and C2.
ReplyDeleteLet 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.