Question

In figure 3.78, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4,MD = 8 find DN
(2) If RS = 18, MD = 9,DN = 8 find DS

Answer 1

For diagram refer to the Attachment 

For (i)⇒
When chord of the circle Intersect internally , then the product of the segment of the chords are equal.

∴ MD× MN = SD × DR
   8 × DN = 4 × 15
DN = (4 × 15)/8
DN = 7.5


For (ii)  ⇒

Let DS be X.
RS = 18 
MD = 9
DN = 8
RD = 18 - X
MD × DN = DS × RD

9 × 8 = X × (18- X)
X² - 18X + 72 =0
X(X -12) - 6(X-12) = 0
Hence , 
X=6 or  X = 12.


Hence SD = 6 or 12 



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Answer 2

Answer:

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