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A and B are the centres of the two externally touching circles.point P is the point of contact AB=13cm, AP =8cm.find the radius of the circle with centre B​

answers: 1
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Answer:

AB=13cm

Radius of circle with center A=8cm

Radius of circle with center A=1cm

Let radius of third circle =r

∠ABC=90°

In △ABC

    AB  

2

+BC  

2

=AC  

2

 

    AC=AD+DC=8+r

    BC=1+r

    AB=13

    13  

2

+(1+r)  

2

=(8+r)  

2

 

    169=(8+r+1+r)×(8+r−1−r)

    =(2r+9)×7

    2r+9=  

7

169

 

    2r=  

7

169

−9

    r=  

14

106

 

r=7.57cm

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