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