Let PQ and RS be two parallel chords of a given circle of radius 6 cm lying on the same side of the centre. If the chords subtends angles of 72? and 144? at the centre and the distance between the chords is d, then find the value of (d square).

Asked by samiddhamukherjee | 16th Sep, 2010, 11:50: PM

Expert Answer:

Dear Student,
 
Let the distance of the nearer chord from the center be X cm. Therefore the distance of the farther chord is X + d cm.
 
 
From the figure we get,
 
cos(36o) = (X + d)/6    ---------(1)
 
and
 
cos(72o) = (X)/6          ---------(2)
 
From (2) we get,
 
X = 6cos(72o)
 
Putting this value in (1) we get
 
6cos(36o) = 6cos(72o) + d
 
=> d = 6(cos(36o) - cos(72o))
 
Calculating the value of cos(36o) and cos(72o) from trigonometric ratios table, we get
cos(360) = 0.809
 
cos(72o) = 0.309
 
=> d = 6(0.809 - 0.309)
 
=> d = 6 x 0.5
 
=> d = 3.
 
 
Regards Topperlearning.

Answered by  | 17th Sep, 2010, 12:33: AM

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