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A quadrilateral ABCD is drawn around a circle so that all four of its sides touch the circle. If AB = 9 cm, BC = 12 cm and CD = 14 cm, what is the length of AD?

Competition practiceGeometry
  • A13 cm
  • B7 cm
  • C11 cm
  • D17 cm

Step-by-Step Solution

The two tangents drawn from an external point to a circle are equal. Adding the tangent lengths around the quadrilateral gives AB + CD = BC + AD. So 9 + 14 = 12 + AD, and AD = 23 − 12 = 11 cm.
Answer: C) 11 cm

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