If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of t…

Question

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 :

Accepted Answer

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$$\phi $$

= $${4 \over {\sqrt 7 }} + {4 \over {\sqrt 7 }}$$ = $${8 \over {\sqrt 7 }}$$

Solutions · 1