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Hey Mate...
I know this question is from Maths class 10 chapter circles.
So, from theorem
PQ=PR----------------(1)
and also AQ=AB------------(2) and BC=CR------------(3)
AC=AB+BC=AQ+CR----------(4)[from equation (2) & (3)]
so, Perimeter of triangle APC
=AP+PC+AC
from equation (4):-
=AP+PC+(AQ+CR)
=(AP+AQ)+(PC+CR)
=PQ+PR (∵ PQ=AP+AQ and PR=PC+CR)
Now, from equation(1)
=PQ+PQ
=2PQ
Hope this answer helps this you...