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Incircle of ABC touches the sides AB at P, BC at Q and CA at R. If AB = 10 cm and CR = 6 cm then the semiperimeter of ABC (in cm) is

Incircle of ABC touches the sides AB at P, BC at Q and CA at R. If AB = 10 cm and CR = 6 cm then
the semiperimeter of ABC (in cm) is

Question Image
Grade:10

1 Answers

Rajat
213 Points
2 years ago
It can be observed that
AP=AR, BP=BQ, CQ=CR since these are the tangents to the incircle from points A,B and C respectively. Perimeter = AB+BC+CA= (AP+BP)+(BQ+CQ)+(CR+AR)=(AP+AR)+(CR+CQ)+(BP+BQ)=2AP+2BP+2CR=2(AB+CR)=2(10+6)=2(16)=2(SEMIPERIMETER)
Therefore, SEMIPERIMETER= 2(16)/2=16 units

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