Geometry Problem
Click the figure below to see the complete problem 475 about Tangent Circles, Secant, Tangent, Parallel.
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Complete Problem 475
Level: High School, SAT Prep, College geometry
Sunday, July 18, 2010
Problem 475: Tangent Circles, Secant, Tangent, Parallel
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Drag diameter of circle C2 and let X and Y the interseptions of this line with C1 and C2 respectively.
ReplyDelete- 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
^^
ang ABO1 = ang O1AB ( AO1B isoceles )
ReplyDeleteang ACO2 = ang O2AC ( AO2C isoceles )
=>
ang ABO1 = ang ACO2
=>
L2BA = L1CA ( 90° - ABO1, ... )
as corresponding angles
=>
L2//L1
Draw common tangent at A to cut L1 at X and L2 at Y
ReplyDeleteTriangles ACX and ABY are both isoceles and the result follows:
Sumith Peiris
Moratuwa
Sri Lanka