Geometry Problem

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

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Complete Problem 466

Level: High School, SAT Prep, College geometry

## Tuesday, June 29, 2010

### Problem 466: Concentric Circles, Secant, Congruence, Measurement

Labels:
concentric circles,
congruence,
measurement,
secant

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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.