A inscribe circle in a ΔABC in such way it can touch the sides AB, BC,CA at P,Q, and R respectively and AP = 7cm , CR = 6cm and BC = 12 cm then find the perimeter of the ΔABC. एक Δ ABC में एक अंत:वृत्त इसप्रकार है की वह भुजा AB,BC और CA को क्रमशः P, Q, और R पर स्पर्श करता हैं और AP = 7cm, CR = 6 सेमी और BC = 12 सेमी है तो Δ ABC की परिमाप ज्ञात कीजिए।

For an incircle touching sides AB, BC, CA at P, Q, R respectively: AP = AR = 7 cm (tangents from A), CR = CQ = 6 cm (tangents from C), BQ = BP = 12 cm (tangents from B, since BC = BQ+CQ = BQ+6 = 12, so BQ = 6). Wait, BC = 12 is given. BQ+CQ = 12. If CQ=6, then BQ=6. So BP=6, BQ=6. Perimeter = AB+BC+CA = (AP+PB)+(BQ+CQ)+(CR+RA) = (7+6)+(6+6)+(6+7) = 13+12+13 = 38 cm. ✓