RRB RPF RPSF SI and CONS Model Papers 2 with solutions

Question : 10 of 120

Marks: +1, -0

An equilateral triangle and a regular hexagon are inscribed in a given circle. If a and b are the lengths of their sides respectively, then which one of the following is correct.

$a ^ { 2 } = 2 b ^ { 2 }$
$b ^ { 2 } = 3 a ^ { 3 }$
$b ^ { 2 } = 2 a ^ { 2 }$
$a ^ { 2 } = 3 b ^ { 2 }$

Validate

Solution:

(d) We know altitude of equilateral ΔABC is

√3/2

∴Length of OC =

= \ { √ { 3 } }/ { 2 } a × { 2 } /{ 3 } = { a }/ { √ { 3 } } =

radius
Also,

D F = b ⇒ D E = { b }/ { 2 }

In ΔODE,

\cos 60° = { D E }/ { O D } = { b / 2 }/ { a / √ { 3 } }

⇒ { 1 } /{ 2 } = { √ { 3 } b }/ { 2 a }⇒ a =√ { 3 } b

∴

a ^ { 2 } = 3 b ^ { 2 }

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