Multiple choice

From an external point P, tangents PA and PB are drawn to circle O. CD is tangent to the circle at E. If AP = 16 cm, find the perimeter of (\triangle PCD).

  1. 24 cm

  2. 30 cm

  3. 32 cm

  4. 28 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From external point P, PA = PB = 16 cm (tangents from same point). By tangent properties: perimeter of triangle PCD = PC + CD + PD = (PC + CE) + (ED + PD) = PC + PD + CE + ED. Since PC = PA and PD = PB, and CE = ED (tangents from same point E), perimeter = PA + PB + 2CE = 16 + 16 + 2CE. But CE = CD/2 and CD is tangent segment. Actually, perimeter = 2 × AP = 32 cm. Option C is correct.

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