Monday, July 26, 2010

Problem 480: Triangle, Circle, Center, Altitude, Angle, Circumcenter

Geometry Problem
Click the figure below to see the complete problem 480 about Triangle, Circle, Center, Altitude, Angle, Circumcenter.

Problem 480: Triangle, Circle, Center, Altitude, Angle, Circumcenter
See also:
Complete Problem 480

Level: High School, SAT Prep, College geometry

2 comments:

  1. join A to O, draw OT perpendicular to AB ( T on AB )
    ang BCD = 90° - ß = 1/2 arc ACB (1)
    ang AOB = arc ACB =>
    ang AOT = 1/2 arc ACB (2)
    from (1) & (2)
    ang BCD = ang AOT =90°-α =90°-ß (3)( AT=TB,OT perpen )
    from (3) =>

    α = ß

    ReplyDelete
  2. I take the E point of maximum arc AB (not arc ACB).Is <BCD=<AEB=γ,then β+γ=90.
    But <AOB=2.<AEB=2γ,so 2α+2γ=180 or α+γ=90. Therefore α=β.

    ReplyDelete