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      Question

      In the figure given below, a circle is inscribed in a

      triangle ABC. If AB = 18 cm, BC = 14 cm and AC = 16 cm, then find the length of YC.
      A 6 cm Correct Answer Incorrect Answer
      B 4 cm Correct Answer Incorrect Answer
      C 2 cm Correct Answer Incorrect Answer
      D 8 cm Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let YA = 'a' cm

      YC = AC - YA = (16 - a) cm

      We know that the tangents drawn from an external point to a circle are equal.

      So, ZC = YC = (16 - a) cm

      BZ = BC - ZC = 14 - (16 - a) = (a - 2) cm

      Again, BX = BZ = (a - 2) cm

      AX = AB - BX = 18 - (a - 2) = (20 - a) cm

      Again, AX = YA

      So, 20 - a = 'a'

      Or, 2a = 20

      Or, 'a' = 10

      Therefore, YC = 16 - 10 = 6 cm

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