Saturday, September 22, 2012

Problem 805: Stewart's Theorem, Triangle, Sides, Cevian, Metric Relations, Measurement

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

Click the figure below to see the complete problem 805.

Online Geometry Problem 805: Stewart's Theorem, Triangle, Sides, Cevian, Metric Relations, Measurement.

1 comment:

  1. In triangle ADC,
    b^2 = x^2 + m^2 - 2 x m cos(ADC)

    In triangle BDC,
    a^2 = x^2 + n^2 - 2 x n cos(BDC)

    Since cos(ADC) + cos(BDC) = 0,
    (x^2 + m^2 - b^2) / (2xm) + (x^2 + n^2 - a^2) / (2xn) = 0
    n(x^2 + m^2 - b^2) + m(x^2 + n^2 - a^2) = 0

    a^2 m + b^2 n
    = (m+n) x^2 + mn(m+n)
    = x^2 c + cmn

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