Question
Two chords, AB and CD, of a circle intersect at an external
point E. Given that the lengths of BE and DE are 12 cm and 8 cm, respectively, and the total length of chord AB is 36 cm, determine the length of chord CD.Solution
BE = 12 cm, DE = 8 cm, and AB = 36 cm
From the secant theorem:
AE X BE = CE X DE .... (I)
AE = AB + BE = 36 + 12 = 48 cm
Put the value of AE in equation (I) , we get,
48 X 12 = CE X 8
Or, CE = 48 X 12 X (1/8)
So, CE = 72 cm
Therefore, the length of the chord CD = CE - DE = 72 - 8 = 64 cm
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