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In the figure given below AG and BG are diameters of two circles with radii 2 cm and 6 cm respectively. G is the only point of contact of the two circles. BC is a tangent of length 12 cm to the bigger circle and BF is perpendicular to the line AC. Find the length of CF.
  • a)
    4.8cm
  • b)
    6.4cm
  • c)
    7.2cm
  • d)
    9.6cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
In the figure given below AG and BG are diameters of two circles with...
In the ΔABC, ∠ABC = 90°
AB = 4 + 12 = 16cm,
BC = 12cm
∴ AC = √ (162 + 122) = 20 cm.
ΔABC and ΔAFB are similar (∠AFB = ∠ABC and ∠FAB = ∠BAC)
AF/AB = AB/AC => AF/16 = 16/20
AF = 12.8 cm
Therefore, CF = 20 - 12.8 = 7.2 cm
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