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A circular ring of radius 3cm hangs hori...

A circular ring of radius 3cm hangs horizontally form a point 4cm vertically above the centre by 4 strings attached at equal intervals to its circumference. If the angle between two consecutive strings be `theta` , then `costheta` is equal to `4/5` (b) `4/(25)` (d) `(16)/(25)` (d) none of these

Text Solution

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Let P be the point from which the ring is hanging .Also ,let the strings are attached to the point A,B,C and D at the ring .

In the figure ,
OP =4
OA =OB=OC=OD=3
AP = BP =CP =DP `=sqrt(3^2+4^2)=5`
ABCD is square of sides lenght `3sqrt(2)` cm Now in triangle PDB.
`sin""(theta)/2=(1/2 BC)/(BP)=(3/sqrt(2))/5=(3)/(5sqrt(2))`
`therefore cos theta = 1-2 sin ^2""(theta)/(2)=16/25`
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