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Question

A ring, 10 cm in diameter, is suspended from a point 12 cm above its centre by 6 equal strings attached to its circumference at equal intervals. The cosine of the angle between consecutive strings is


A

213236

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B

313338

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C

119345

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D

None of these

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Solution

The correct option is B

313338


Let L be the centre of the circle ABCDEF whose diameter be 10 cm. M is the point 12 cm above it and AM, BM, CM, DM, EM, and FM, are strings which hang from M and are attached to it at points A,B,C,D, E and F.
Length of string MB
=(ML)2+(LB2)=122+52=13cm.
When circumference is divided in six equal parts each chord
= Radius
Hence BC=5cm.

cos(BMC)=MB2+MC2BC22.MB×MC=(13)2×(13)2(5)22×13×13=313338


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