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.

4 comments:

  1. idk how to prove this segment someone help me

    ReplyDelete
  2. 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. P the point where circle meet AE, T the point where circle meet BC

    ReplyDelete