Monday, May 19, 2008

Elearn Geometry Problem 66



See complete Problem 66
Triangle, Excircle, Tangents, Geometric Mean. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.
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5 comments:

  1. AnonymousFebruary 23, 2010 at 12:31 PM

    idk how to prove this segment someone help me

    ReplyDelete
  2. c .t . e. oApril 1, 2010 at 11:30 AM

    name P, OP meet AE
    POE = A/2 (perpendicular sides)
    POC = C/2 (POT = C, PCTO cyclic, T tg points to BC, OC
    bisector of kite )
    =>
    COE = A/2 + C/2 (1)
    OBD = (180 - B)/2 = 90 - B/2 = A/2 + C/2 (2)
    (1) & (2) =>

    COE = OBD (3)

    E = D (4) (AED isoceles,AO bisector + altit)

    from (3) & (4)
    ▲COE ~ ▲OBD
    =>
    (DE/2)/e = d/(DE/2)

    DE = 2√d∙e
    -------------------------------------------

    ReplyDelete
  3. c.t.e.oNovember 24, 2015 at 6:05 AM

    P the point where circle meet AE, T the point where circle meet BC

    ReplyDelete
  4. Sumith PeirisJuly 22, 2017 at 4:36 AM

    O is the excentre and OA bisects < A so OD = OE

    Tr. s BOD and COE have as angles 90-A/2, 90-B/2 and 90-C/2 and are hence similar

    So DO/d = e/OE and since DO = OE = DE/2, the result follows

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete

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