A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively. If AB - BC = 4 cm, AB - AC = 2 cm and the perimeter of ΔABC = 36 cm, then PB + AR (in cm) is:
Show answer & explanation
Correct answer: C
Explanation
Given:
AB − BC =
AB − AC =
Measurement =
According to the sources:
For the inscribed circle
PB = s − BC
AR = s − AC
where s = semiperimeter
Let's assume
AB = a, BC = b, AC = c
a − b = 4 → b = a −
a − c = 2 → c = a −
Measurement
a + b + c =
a + (a − 4) + (a − 2) =
3a − 6 =
3a =
a =
b =
c = 12
Half measure(s) = 36/2 =
PB = s − BC= 18 − 10=
AR = s − AC = 18 − 12 =
PB + AR= 8 + 6=
PB + AR = 14 cm.