SSC CGL Tier II 25 Oct 2015 Paper 1

Question : 94 of 100

Marks: +1, -0

AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between them is 3 cm, then the diameter of the circle is

$2√21$ cm.
$√21$ cm.
$2 √29$ cm.
$√29$ cm.

Validate

Solution:

(3)

OA = OC = radius
OE ⊥ AB
OF ⊥ CD
∴ AE = EB = 5 cm.
CF = FD = 2 cm.
OE = x cm.
In ΔOAE,

{OA}^{2}= {AE}^{2}+ {OE}^{2}

⇒{OA}^{2}=5^{2}+x^{2}.....(i)

In ΔOCF,

{OC}^{2}=2^{2}+( {x}+3)^{2}.....(ii)

∴ 5^{2}+x^{2}=2^{2}+(x+3)^{2}

⇒ 25+x^{2}=4+x^{2}+6 x+9

⇒ 6 x=25-13=12

⇒ x=\ {12}/{6}=2 {cm}

∴{OA}^{2}=25+x^{2}=25+4=29

∴{OA}=√{29} {cm} .

∴

Diameter of circle

=2√29\cm

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