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