Diameter AB of a circle with center O is produced to a point P such that PO = 16.8 cm. PQR is a secant that intersects the circle at Q and R such that PQ = 12 cm and PR = 19.2 cm.The length of AB (in cm) is :
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Correct answer: D
Explanation
The correct answer is option 4 i.e 14.4
We know that,
⇒ PQ × PR = PB × PA
Let 'r' be the radius of the circle.
⇒ 12 × 19.2 = (PO - r) × (PA + r)
⇒ 230.4 = (16.8 - r)(16.8 - r)
⇒ 230.4 = 282.24 - r2
⇒ r2 = 51.84
⇒ r = 7.2 cm
⇒ AB = 2r ⇔ 2(7.2)
⇒ 14.4 cm