Geometry Problem

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

Click the figure below to see the complete problem 930.

## Friday, September 27, 2013

### Geometry Problem 930: Acute Triangle, Altitudes, Circles, Diameter, Angle, Measure

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http://img809.imageshack.us/img809/9952/smy9.png

ReplyDeletenote that BFDC is cyclic quadrilateral => AF.AB=AD.AC

but AF.AB=AG^2 and AD.AC=AE^2… ( relation in right triangles AGB and AEC)

so AG=AE=AH

draw circle centered A, radius=AG

Observe that ∠ (HGE)= ½∠ (HAE)= ½(180-2*55)= 35 degrees