Tuesday, January 28, 2014

Geometry Problem 970: Equilateral Triangle, Circumcircle, Secant, Metric Relations

Geometry Problem
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 970.

Online Geometry Problem 970: Equilateral Triangle, Circumcircle, Secant, Metric Relations

2 comments:

  1. Let BD=y.

    DE×DA=DB×DC
    y(x+y)=12

    In ΔABD, using cosine law,
    36=x²+y²+xy=x²+y(x+y)=x²+12

    x²=24
    x=2√6

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  2. Let BD = p

    From similar triangles p(p+x) = 2(2+4) = 12...(1)
    From Pythagoras AD^ 2 = 3x^2/4 + (p+x/2)^2 ....(2)

    (2) - (1) ; x^2 = AD^2 - 12 = 24

    so x = sqrt 24 = 2sqrt6

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