Answer :
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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