Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the problem 744 details.

## Sunday, April 29, 2012

### Problem 744: Parallelogram, Circle, Diameter, Chord, Congruence, Triangle

Labels:
chord,
circle,
congruence,
diameter,
parallelogram

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http://img191.imageshack.us/img191/1969/problem744.png

ReplyDeleteDraw GN//AB ( see sketch)

Since GF=GH => ∠ (FBG)= ∠ (GBH)

We also have ∠ (BGA)= ∠ (NBG)= ∠ (GBH)= ∠ (GBA)….(Alternate angles)

So triangles BNG isosceles and NB=BA=NG=4

In right triangle BGM, GN is a median and BM= 2*BN= 8

So CM= BM-BC= 3