Q12 of 52 Page 160

In the figure 7.49, two circles with centre O and P are touching internally at point A. If BQ = 9, DE = 5, complete the following activity to find the radii of the circles.

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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