Sunday, September 26, 2010

Problem 522: Right Triangle, Circle, Diameter, Tangent

Geometry Problem
Level: High School, SAT Prep, College geometry.
Click the figure below to see the complete problem 522 about Right Triangle, Circle, Diameter, Tangent.

Problem 522: Right Triangle, Circle, Diameter, Tangent

4 comments:

  1. ▲ADE ~ ▲ABE => ED/AE = BE/x
    ▲EDC ~ ▲AEC => ED/AE = DC/5
    => x = 5

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  2. http://ahmetelmas-geo-geo-antonio.blogspot.com/2010/09/prb522.html

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  3. Because FD // BC, FE = DE = m say

    If also BE = DC = p and AE = n

    p/m = x/n = 5/n since Tr.s BEF and ABE are similar and DEC and ACE are similar

    So x = 5

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  4. Solution 2

    FD//BC, ODEC is a kite as before.

    So AE bisects < BAC

    So x/BE = AC/5 or x = AC.BE/5 = CD.AC/5 = 25/5 = 5

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete