Wednesday, November 3, 2010

Problem 536: Intersecting Circles, Chord, Perpendicular. Level: High School, SAT Prep, College Geometry

Geometry Problem
Click the figure below to see the complete problem 536 about Intersecting Circles, Chord, Perpendicular.

Problem 536: Intersecting Circles, Chord, Perpendicular. Level: High School, SAT Prep, College Geometry
Go to Complete Problem 536

2 comments:

  1. extend AC to G on circle O, => BCG isoceles
    => AD = DC + CG = BC + BC

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  2. Let E is the point of intersection of AC to circle O.
    Connect OO’ and note that OO’ is the perpendicular bisector of AB

    1. We have Angle(BEC)=angle (O’OA)
    And angle(ACB)=2 *angle(O’OA)=angle(BEC)+angle(CBE)
    So angle(CBE)=angle(O’OA)=angle(CBE)
    Triangle BCE isosceles and CB=CE

    2. Since AE is a chord of circle O so D is the midpoint of AE
    We have Area(ADO)=Area(DOC)+Area(COE)
    All above triangles have the same height so AD=DC+CE
    Or AD=BC+CB

    Peter Tran

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