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HorseObsessed
Lv 5
HorseObsessed asked in Science & MathematicsMathematics · 8 years ago

In the diagram of circle O, chord AB bisects chord CD at E. If AE=4 and EB=9, what is the length of CD? (pic)?

Please show work.

http://i40.tinypic.com/2rpczva.png

1 Answer

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  • Learner
    Lv 7
    8 years ago
    Favorite Answer

    i) This is a direct application of a theorem on circles. One theorem on circles states that "If two chords of a circle intersect either internally or externally, then the intercepted segments of the respective chords forms a rectangle." [That is the product of the corresponding intercepted segments are equal].

    ii) As such here, CE x ED = AE x EB

    ==> x² = 4 x 9 = 36

    Solving x = 6 units.

    So CE = 6 + 6 = 12 units

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