A circle is inscribed in ∆ABC, toucing AB, BC and AC are the points P, Q and R, respectively. If AB - BC = 4 cm, AB - AC = 2 cm, and the perimeter of ∆ABC = 32 cm, then AC (in cm) = ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 32/3
Calculations:
AB - BC = 4 cm
BC = AB - 4
AB - AC = 2 cm
AC = AB - 2
Perimeter of triangle ABC = AB + BC + AC = 32
⇒ AB + AB - 4 + AB - 2 = 32
⇒ 3AB = 38
⇒ AB = 38/3
Now we have AC = AB - 2
⇒ AC = 38/3 - 2 = 32/3 cm