JEE MAIN - Mathematics (2017 - 8th April Morning Slot - No. 16)
If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $${\cos ^{ - 1}}\left( {{1 \over 7}} \right)$$ and sec$$-$$1 (7) at the center respectivey, then the distance between these chords, is :
$${4 \over {\sqrt 7 }}$$
$${8 \over {\sqrt 7 }}$$
$${8 \over 7}$$
$${16 \over 7}$$
Explanation
_8th_April_Morning_Slot_en_16_1.png)
Since cos2$$\theta $$ = 1/7 $$ \Rightarrow $$ 2 cos2 Q $$-$$ 1 = 1/7
$$ \Rightarrow $$ 2 cos2$$\theta $$ = 8/7
$$ \Rightarrow $$ cos2 $$\theta $$ = 4/7
$$ \Rightarrow $$ cos2$$\theta $$ = $${4 \over 7}$$
$$ \Rightarrow $$ cos2$$\theta $$ = $${2 \over {\sqrt 7 }}$$
Also, sec2$$\phi $$ = 7 = $${1 \over {2{{\cos }^2}\phi - 1}}$$ 7
= cos2$$\phi $$ $$-$$ 1 = $${1 \over 7}$$
= 2 cos2 $$\phi $$ = $${8 \over 7}$$
= cos$$\phi $$ = $${2 \over {\sqrt 7 }}$$
P1P2 = r cos$$\theta $$ + r cos$$\phi $$
= $${4 \over {\sqrt 7 }} + {4 \over {\sqrt 7 }}$$ = $${8 \over {\sqrt 7 }}$$
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