Q. 124.1( 17 Votes )

# <span lang="EN-US

Let the radius of the bigger circle be R and that of smaller circle be r.

OA, OB, OC and OD are the radii of the bigger circle

OA = OB = OC = OD = R

PQ = PA = r

OQ = OB -BQ =R – 9

OE = OD - DE = R – 5

As the chords QA and EF of the circle with centre P intersect in the interior of the circle, so by the property of internal division of two chords of a circle,

OQ × OA = OE × OF

(R- 9) × R = (R- 5) × (R - 5) ……… ( OE = OF)

R2 - 9R = R2 - 10R + 25

R = 25

AQ = 2r = AB – BQ

2r = 50 - 9 = 41

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