SSC CGL 7 06 2019 Shift 2 Paper

Question : 53 of 100

Marks: +1, -0

AB is diameter of a circle with centre 0. CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6cm and AG= 8cm, then the length of BC is:

$2√5$ cm
$6 √6$ cm
$2√6$ cm
$6√5$ cm

Validate

Solution:

Let

\ {GC}=\ {x}

We know,

B C^{2}=x(x+8)

.....(i)
(i) Also,

\ {BC}^{2}=(\ {x}+8)^{2}

-(12)^{2}

......(ii)
equating (i) and (ii)

x(x+8)=(x+8)^{2}-144

on solving,

x=10

by equation (i), Now,

\ {BC}=\√{10(18)}

=6 \√{5} \ {\cm}

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