From the figure,
AQ=AR
[Tangents drawn from a point outside the circle are equal in length]
⇒AQ=AC+CR(∵AR=AC+CR)
CR=CP
[Tangents drawn from a point outside the circle are equal in length]
∴AQ=AC+CP...(i)
Also, AQ=AB+BQ
But, BQ=BP
[Tangents drawn from a point outside the circle are equal in length]
∴AQ=AB+BP...(ii)
Adding equations (i) and (ii),
2AQ=AC+CP+BP+AB
2AQ=Perimeter of ΔABC
∴Perimeter of ΔABC=2×15=30 cm