Multiple choice

Diameter AB of a circle with centre O is produced to a point P such that PO = 16.8 cm. PQR is a secant which intersects the circle at Q and R such that PQ = 12 cm and PR = 19.2 cm. The length of AB (in cm) is:

  1. 14.4

  2. 14.2

  3. 15.2

  4. 15.8
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A Correct answer
Explanation

By the secant theorem, for external point P, PB × PA = PQ × PR where A and B are diameter endpoints. Given PO = 16.8 cm, let AB = d. If P is beyond B: PB = 16.8 - d/2 and PA = 16.8 + d/2. So (16.8)² - (d/2)² = 12 × 19.2 = 230.4. Solving: 282.24 - d²/4 = 230.4, giving d² = 207.36 and d = 14.4 cm.

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