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 :
Answer & explanation
Correct answer: option 4
We know that ,
PB × PA = PQ × PR
Let us consider that radius = OA = OB = r cm
( 16.8 - r ) × ( 16.8 + r ) = 12 × 19.2
( 16.8)² - r² = 230.4
282.24 - 230.4 = r²
r² = 51.84
r = 7.2
AB = 2r = 2 x 7.2 = 14.4 cm