Chords AB and CD of a circle intersect inside the circle at point F. If m(AF) 2.4 cm. m(BF) 1.8 cm, and m(CD) = 5.7 cm. What is the length (in cm) of the longer of the two line segments, CF and DF?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 4.8.
AB and CD are two chords that intersect inside the circle at F.
CF = x cm and DF = (5.7 - x) cm
AF × FB = CF × DF
⇒ 2.4 × 1.8 = x(5.7 - x)
⇒ 5.75x - x2 = 4.32
⇒ x2 - 5.7x + 4.32 = 0
⇒ (x - 0.9)(x - 4.8) = 0
⇒ x = 0.9 or 4.8
CF (x) = 4.8 cm
Therefore, the longer segment (CF) is 4.8 cm.