Multiple choice

Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If PC = 12 cm, and BP = 10 cm, then the length of AB (in cm) is

  1. 4.4

  2. 6

  3. 5

  4. 5.4
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A Correct answer
Explanation

By the power of a point theorem (secant-tangent theorem): PC² = PA × PB, where PA = AB + BP. Given PC = 12 and BP = 10: 12² = (AB + 10) × 10, so 144 = 10(AB + 10), giving 14.4 = AB + 10, thus AB = 4.4 cm. The tangent-secant theorem relates the tangent length to the segments of the secant.

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