In the adjoinig figure, three circles with centres A,B,C touch one another extenally. If `AB=5 cm, BC =7` can and CA = 6 cm, then length of radius of circle with centre A.

Explanation

As per question, `AB=5` cm.
`therefore AP+ BP=5[because` two circles with centres A and B touch each other externally at P] …….(1)
Similarly, `BC= 7 cm`
`therefore CR+ BR=7 cm …….(2)`
`and CA =6cm, therefore AQ + CQ =6 cm`
or, `AQ+ CR=6 cm.........(3)`
`[becauseCQ=CR,` radii of same circle.]
Then from (2) and (3) we get,
`BR-AQ =1 cm.`
or, `BP- AP=1cm [because BR=BP and AQ =AP].....(4)`
Now, subtracting (4) from (1) we get,
`2AP =4 cm or, AP =4/2cm =2 cm`
`therefore` the length of the radius of the circle with centre A =2 cm.