Correct Answer: Option C

Explanation

From the figure,

  ∠ XMN = ∠ XZY

  Angle X is common

  So, ∠ XNM = ∠ XYZ

  Then from the angle relationship

  \(\frac{XM}{XZ}\) = \(\frac{XN}{XY}\) = \(\frac{MN}{ZY}\)

  XM = 8, XZ = 12 + 4 = 16,

  XN = 12, XY = 8 + YM

  \(\frac{8}{16}\) = \(\frac{12}{(8 + YM) }\)

  Cross multiply

  8(8 + YM) = 192

  64 + 8YM = 192

  8YM = 128

  YM = \(\frac{128}{8}\)

  = 16cm

There is an explanation video available below.

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