Multiple choice

Let PAB be a secant to a circle intersecting the circle at A and B. Let PT be the tangent segment. If PA = 9 cm and PT = 12 cm, then what is AB equal to?

  1. 5 cm

  2. 6 cm

  3. 7 cm

  4. 9 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Tangent-secant theorem: PT^2 = PA * PB. 12^2 = 9 * PB. 144 = 9 * PB. PB = 16. AB = PB - PA = 16 - 9 = 7.

AI explanation

By the tangent-secant theorem, the square of the tangent length equals the product of the secant lengths, so PT squared equals PA multiplied by PB. Substituting the given values gives 144 = 9 multiplied by PB, making PB equal to 16 cm. Since PB is the total length from P to B, AB is PB minus PA, yielding 16 minus 9, which is 7 cm.

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