SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 84 of 100

Marks: +1, -0

O is the circumcentre of the isosceles DABC. Given that AB = AC = 17 cm. and BC = 6 cm. The radius of the circle is

Solution:

(1)

AB = AC = 5 cm. (We have assumed to reach answer)
AD ⊥ BC
BD = DC = 3 cm.

{AD}=√{ {AB}^{2}- {BD}^{2}}

=√{5^{2}-3^{2}}=√{25-9}=√{16}

=4 {cm} .

Let, OA = OC = r cm.
OD = (4 – r) cm.
In ΔOCD,

{OC}^{2}= {OD}^{2}+ {DC}^{2}

⇒ r^{2}=(4-r)^{2}+3^{2}

\⇒ r^{2}=16+r^{2}-8 r+9

\⇒ 8 r=25 ⇒ r= {25}/{8}=3.125

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