38. If two parallel chords of a cir...
Question

# 38. If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and suutch angles cose and sec (7) at the centre respectively, then the distance between these chords, is: [JEE Main 2017) (A) (B) (98 (D) 16

JEE/Engineering Exams
Maths
Solution
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distance between chords = Radius Cos(subtended angle/2) by chord1 + Radius Cos(subtended angle/2) by chord 2 Radius = Diameter ( / 2=4 / 2=2 ) ( =2 cos left(theta_{1} / 2right)+2 cos left(theta_{2} / 2right) ) ( theta_{1}=operatorname{Cos}^{-1}(1 / 7) Rightarrow cos theta_{1}=1 / 7 ) ( theta_{2}=operatorname{Sec}^{-1} 7 Rightarrow operatorname{Sec} theta_{2}=7 Rightarrow 1 / operatorname{Cos} theta_{2}=7 Rightarrow operatorname{Cos} theta_{2}=1 / 7 ) Applying ( cos 2 theta=2 cos ^{2} theta-1 Rightarrow cos ^{2} theta=(1+cos 2 theta) / 2 ) Putting ( theta=theta_{1} / 2 ) ( cos ^{2}left(theta_{1} / 2right)=(1+1 / 7) / 2=4 / 4 ) ( Rightarrow cos left(theta_{1} / 2right)=2 / sqrt{7} ) Putting ( theta=theta_{2} / 2 ) ( cos ^{2}left(theta_{2} / 2right)=(1+1 / 7) / 2=4 / 7 ) ( Rightarrow cos left(theta_{1} / 2right)=2 / sqrt{7} ) ( 2 cos left(theta_{1} / 2right)+2 cos left(theta_{2} / 2right)=2 * 2 / sqrt{7}+2 * 2 / sqrt{7} ) ( =4 / sqrt{7}+4 / sqrt{7} ) ( =8 / sqrt{7} )
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