Sunday, July 18, 2010

Problem 475: Tangent Circles, Secant, Tangent, Parallel

Geometry Problem
Click the figure below to see the complete problem 475 about Tangent Circles, Secant, Tangent, Parallel.

Problem 475: Tangent Circles, Secant, Tangent, Parallel
See also:
Complete Problem 475

Level: High School, SAT Prep, College geometry

2 comments:

  1. Drag diameter of circle C2 and let X and Y the interseptions of this line with C1 and C2 respectively.

    - Angles YBA and XCA are 90°.
    - tr AYB and tr AXC are then similar.
    - thus <AYB = <AXC.
    - <C = <B (semiinscripted angle theorem)
    - L1 // L2 follows

    ^^

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  2. ang ABO1 = ang O1AB ( AO1B isoceles )
    ang ACO2 = ang O2AC ( AO2C isoceles )
    =>
    ang ABO1 = ang ACO2
    =>
    L2BA = L1CA ( 90° - ABO1, ... )
    as corresponding angles
    =>
    L2//L1

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