SSC CGL 9 Aug 2015 Shift 1 Paper

Question : 114 of 200

Marks: +1, -0

A square is inscribed in a quarter- circle in such a manner that two of its adjacent vertices lie on the two radii at an equal distance from the centre, while the other two vertices lie on the circular arc. If the square has sides of length x, then the radius of the circle is

$√2$ x
${16x}/{π+4}$
${2x}/√π$
${√5x}/√2$

Validate

Solution:

OE = OF
EF = x units
∴ From DOEF,
2

OE^2

EF^2

⇒

√2

× OE = EF = x
⇒ OE =

x/√2

BE = diagonal of square EFBC =

√2x

∴ OB =

√{OE^2+EB^2}

√{(x/√2)^2+(√2x)^2}

√{x^2/2+2x^2}

√{{x^2+4x^2}/2}

√{{5x^2}/2}

{√5x}/√2

units

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