See complete Problem 93

Similar Triangles, Circumcircles, Parallelogram. Level: High School, SAT Prep, College geometry

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## Monday, May 19, 2008

### Geometry Problem 93

Labels:
circle,
circumcenter,
circumcircle,
parallelogram,
similarity,
triangle

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1. If angle DAC is x, then Angle GMC=Angle EFG=Angle BDF=x

ReplyDelete2. Then angle EO2G=2x; Angle O1OC=2x (According to the rule that the central angle is two times that of peripheral angle on a circle)

3. According to the same rule angle GO3C=2x= angle BO1O2; then Angle OO1O2= Angle GO3O=180-2x

4. Because alternate angles are same; the O1OO3O2 is a parralelogram