Proposed Problem
Click the figure below to see the complete problem 334 about Cyclic Quadrilateral, Perpendiculars to Diagonals.
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Complete Problem 334
Level: High School, SAT Prep, College geometry
Wednesday, August 5, 2009
Problem 334. Cyclic Quadrilateral, Perpendiculars to Diagonals
Labels:
cyclic quadrilateral,
diagonal,
perpendicular
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all tr are similar to each other( ang to perpen sides)
ReplyDeleteAE/AF = ED/DM = EC/CH = BE/BG
or BG/AF = CH/DM = ...
or BG*DM = AF*CH
To prove that F, M, H, G lie in the same circle
ReplyDeleteJoin MH, GE HMCD is a cyclic quadrilateral with
ReplyDeleteexterior ∠GMH = interior opposite ∠HDC = ∠BDC
GFBA is a cyclic quadrilateral with
exterior ∠GFH = interior opposite ∠BAG = ∠BAC
But ∠BDC = ∠BAC (angles in the same segment) So ∠GMH = ∠GFH and G,F,M,H are concyclic