SSC CGL Tier II 21 Sep 2014 Paper

Question : 27 of 100

Marks: +1, -0

Two chords of lengths a metre and b metre subtend angles 60° and 90° at the centre of the circle respectively. Which of the following is true ?

Solution:

(1)

Radius of circle = r units
In ΔOCD, ∠COD = 90°

∴{CD}^{2}= {OC}^{2}+ {OD}^{2}

⇒ b^{2}=r^{2}+r^{2}=2 r^{2} ...( {i})

In ΔOAB,
OE ⊥ AB
∠OAB = 60°

{AE}= {a}/{2}

∴ \cos 60°= { {AE}}/{ {OA}}

⇒{1}/{2}= { {a}/{2}}/{r}

⇒{1}/{2}= {a}/{2 r} ⇒ a=r...(ii)

From equations (i) and (ii),

b^{2}=2 a^{2}

⇒ b=√{2} a

Go to Question:

Prev Question

Next Question