CDS Model Paper 3 Mathematics

Let O is centre of big circle, and O′ is centre of smaller circle. Both are touch internally each other.
OA=6‌cm‌O′‌A=4‌cm
Here PR is longest chord of big circle
P.S=

PR

2

OS=AS−OA
=8−6=2cm
In ΔPSO
(PS)2+(OS)2=(OP)2
⇒ (PS)2+(2)2=(6)2
PS=√36−4=√32=4√2
Now,
PS=

PR

2

PR=2×PS=2×4√2=8√2