Find The Length of The Segment of The Tangent Between them

The distance between the centres of two circles with radii 9 cm and 16 cm is 25 cm. The length of the segment of the tangent between them is

  1. 24 cm
  2. 25 cm
  3. 50/3 cm
  4. 12 cm
Anurag Mishra Professor Asked on 20th July 2015 in Maths.
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1 Answer(s)

Answer: (1) 24 cm
Explanation:-
Formula-
(distance between their centres)2 = (difference of their radius)2 + (length of the segment of the tangent)2
Then, (length of the segment of the tangent)2 = (distance between their centres)2 – (difference of their radius)2
According to the question,
(length of the segment of the tangent)2 = (25)2 – (7)2
   = 625 – 49
= 576
(length of the segment of the tangent)2  = 242
length of the segment of the tangent = 24     (square root of both side)
Hence, the length of the segment of the tangent between them is 24 cm.

Anurag Mishra Professor Answered on 20th July 2015.
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