Multiple Choice Question (MCQ)

In the figure, if AE = 3, DE = 5, and CE = 7, then BF equals:

Dandelin Spheres Theory - Math Images

  1. ×

    3.6

  2. ×

    4.0

  3. 4.2

  4. ×

    4.5

  5. ×

    5.0

Collected in the board: Triangle

Steven Zheng posted 1 month ago

Answer


  1. \angle BAF and \angle DAE are complementary angles, which means their sum is 90\degree . Therefore, \triangle AED and \triangle BFA are similar. Similarly, \triangle CFB and \triangle DEC are also similar.

    Therefore, we get the following equations.

    \dfrac{BF}{AF} = \dfrac{AE}{DE} =\dfrac{3}{5}
    (1)

    \dfrac{BF}{CF} = \dfrac{CE}{DE} = \dfrac{7}{5}
    (2)

    Divide (1) by (2), we get

    \dfrac{CF}{AF} = \dfrac{3}{7}
    (3)

    On the other hand,

    CF+AF = CE+AE = 10
    (4)

    Solve the system of equations (3) and (4),

    We get, CF = 3 and AF = 7

    Using the equation (2),

    BF = \dfrac{7}{5}\times CF = \dfrac{7}{5}\times 3 = 4.2




Steven Zheng posted 1 month ago

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