Sunday, August 29, 2010

Problem 515: Triangle, Double Angle, Altitude, Measure

Geometry Problem
Click the figure below to see the complete problem 515 about Triangle, Double Angle, Altitude, Measure.

Problem 515: Triangle, Double Angle, Altitude, Measure

See also:
Complete Problem 515

Level: High School, SAT Prep, College geometry


  1. Locate E on CD s.t. DE=d. Now triangles BAD & BED are congruent with BE=c and /_BED=2α which makes /_EBC=2α-α=α or BE=EC=c. Hence, e=DE+EC=d+c

  2. extend CA to G, AG = AB => ▲GBC isoceles =>
    BD median

  3. Extend AC to the left and locate point E such that AE=c
    Triangle ABE isosceles with angle(AEB)=alpha
    so triangle EBC isosceles and BD is the median of isosceles tri. EBC
    we have DC=DE=DA+AE=d+c

    Peter Tran

  4. Let point E on line AC, and BE=BC.
    Angle BEA=angle BCA=alpha.
    AB=AE, since angle ABE=alpha (2xalpha - alpha).
    Point D=midpoint of EC---> EA+AD=DC (c+d=e)