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= 32 cm, then AC (in cm) = ?
Answer & explanation
Correct answer: option 3
AB - BC = 4 ..(1)
AB - AC = 2 ..(2)
Perimeter of ABC = 32
AB + BC + CA = 32 ..(3)
Adding equations (1), (2) and (3)
32 = 3AB - 6
3AB = 32 + 6
3AB = 38
AB = \(\frac{38}{3}\)
Now,
⇒ AC = AB - 2
⇒ AC = [\(\frac{38}{3}\) - 2]
⇒ AC = \(\frac{32}{3}\) cm
Therefore, AC is \(\frac{32}{3}\) cm.