Geometry Problem

Click the figure below to see the complete problem 456 about Three tangent circles, Center, Chord, Secant, Collinear.

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Complete Problem 456

Level: High School, SAT Prep, College geometry

## Monday, May 17, 2010

### Problem 456: Three tangent circles, Center, Chord, Secant, Collinear

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B, E, C are collinear (from E, EB, EC perpen to comm tg)

ReplyDeleteBDE = BED , ADG = AGD ( DB = BE = r, AD = AG = R )

=>

BED = AGD => BEC//AG (1)

CFE = CEF , AFH = AHF ( CE = CF = r, AH = AF = R )

=>

CEF = AHF => BEC//AH (2)

from (1) & (2)

from A we can draw just one parallel to a line (BEC)

H, A, G are collinear

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Problem 456

ReplyDeleteDesign all common external tangents intersect at P.(P is the radical center of three circles).

Is <DAH=2.<DFH=2.<DFE=<DPE, (PD=PE=PF), <FAG=2.<FDG=2.<FDE=<FPE and <DAF=

180-<DPF (ADPF=cyclic).Then <DAH+<FAG+<DAF=<EPD+<EPF+180-<DPE=180.

Therefore H,A and G are collinear.

APOSTOLIS MANOLOUDIS 4 HIGH SHCOOL OF KORYDALLOS PIRAEUS GREECE