Question

In the figure7.49, 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

Answer 1

Step-by-step explanation:

Answer.......

Let the radius of smaller circle is ( r ) and bigger circle is ( R )

OA = OB = OC = OD = R .......

PQ = PA = r .......

OQ = OB - BQ

= R - 9

OE = OD - DE

OE = R - 5

As the Chord QA and EK of the circle with P center intersect in the interior of the circle

So by the internal division of two chord of circle :

QO × OA = OE × OR

( R - 9 ) × R = ( R - 5 ) ( R - 5 ) .......( OE = OK )

R^2 - 9R = R^2 - 10R + 25

- 9R + 10R = 25

R = 25 ......... Radius of bigger circle.

AQ = 2r = AB - BQ

2r = 50 - 9

2r = 41

r = 41 / 2 = 20.5 .......Radius of smaller circle

Thank you