Geometry Problem

Click the figure below to see the complete problem 529 about Right Trapezoid, Circle, Diameter.

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Complete Problem 529

Level: High School, SAT Prep, College geometry

## Sunday, October 17, 2010

### Problem 529: Right Trapezoid, Circle, Diameter

Labels:
circle,
diameter,
right angle,
trapezoid

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1)draw CG // AB => ▲AGE = ▲FBC => AE = BF

ReplyDelete2)▲AEG ~ ▲AFD ( ang AFD = ang AGE, 90 - FCG & 90 - EGC)

AD/AF = AG/AE

AD/AF = BC/AE

Let M is the intersection of AD to circle O

ReplyDeleteLet N is the projection of point O over chord EF.

Since NO is the mid base of trapezoid ABCD . N is the midpoint of chord EF and segment AB.

(1) BN=AN & NE=NF so AE=BF

(2) Note that CM perpendicular to AD and ABCM is a rectangular so BC= AM

Consider point A and 2 secants AEF & AMD to circle O

We have AE.AF=AM.AD so AE.AF=BC.AD

Peter Tran