#### Question

In the given figure , two circles with centres 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.

#### Solution

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 x r = R - 5 x R - 5 .....(∵ OE = OF)*R*^{2} − 9*R* = *R*^{2} − 10*R *+ 25*R* = 25

AQ = 2*r* = AB − BQ (∵AB = 2*R*)

2*r* = 50 − 9 = 41*r* = \[\frac{41}{2}\] = 20.5

Is there an error in this question or solution?

Solution In the Given Figure , Two Circles with Centres 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. Concept: Surface Area of a Combination of Solids.