Geometry Problem. Post your solution in the comment box below.

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

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## Wednesday, February 18, 2015

### Geometry Problem 1085: Intersecting Circles, Concyclic Points, Cyclic Quadrilateral

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∠GAH

ReplyDelete= ∠CAD

= ∠ADF − ∠ACE

= ∠ABF − ∠ABE

= ∠EBF

= ∠GBH

Hence, ABHG are concyclic.

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Corollary

Since ∠GHB = ∠DAB = ∠DFB

Thus, GH // CF.

Denote ∠DAB = ∠DFB = x and ∠ABE = ∠ACE = y

ReplyDeleteClearly ∠G = x - y = ∠H and so A,G,H,B are concyclic

< ABF = <ADF......(1)

ReplyDelete<ABE = <ACF .....,(2)

(1)-(2) < EBF = < CAD = < GAH

so ABHG is concylic

Sumith Peiris

Moratuwa

Sri Lanka

It also follows that CF and GH are parallel

ReplyDelete