Geometry Problem

Click the figure below to see the complete problem 607.

## Saturday, May 28, 2011

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## Saturday, May 28, 2011

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Problem 607: Intersecting Circles, Triangles, Metric Relations, Measurement

Online Geometry theorems, problems, solutions, and related topics.

Labels:
intersecting circles,
measurement,
metric relations,
triangle

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Isosceles triangles ACF, BCE are similar.

ReplyDeleteCF/CE = AC/BC

CF.CB = CE.CA, and so A,B,F,E are concyclic.

GBA, GFE are secants from G to the circle BAEF.

GB.GA = GF.GE,

x(x+10)= (8).(12),

(x + 5)² = 121,

x+5=11, x=6

< BEC = < BCE = < AFC

ReplyDeleteHence BAEF is cyclic

So 8 x 12 = x(x+10)

Solving the quadratic for positive x

x = 6

Sumith Peiris

Moratuwa

Sri Lanka