Wednesday, August 5, 2009

Problem 334. Cyclic Quadrilateral, Perpendiculars to Diagonals

Proposed Problem
Click the figure below to see the complete problem 334 about Cyclic Quadrilateral, Perpendiculars to Diagonals.

 Problem 334. Cyclic Quadrilateral, Perpendiculars to Diagonals.
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Complete Problem 334
Level: High School, SAT Prep, College geometry

3 comments:

  1. all tr are similar to each other( ang to perpen sides)

    AE/AF = ED/DM = EC/CH = BE/BG
    or BG/AF = CH/DM = ...

    or BG*DM = AF*CH

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  2. To prove that F, M, H, G lie in the same circle

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  3. Join MH, GE HMCD is a cyclic quadrilateral with
    exterior ∠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

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