Two chords AB and CD of a circle intersect at a point F outside the circle. If AF = 12 cm, BF = 4 cm, and CF = 16 cm, find the length of CD.

Explanation

AB =AF-BF =12-4=8 AB=8 If two chords AB and CD of a circle are cut at a point F outside the circle then, AF × BF = CF × DF Let DF be a cm. So, according to the concept, AF × BF = CF × DF 12 × 4 = 16 × a 48 = 16a a = 48/16 a = 3 So, DF = 3 Now, CD = CF - DF CD = 16 - 3 CD = 13 cm