Two circles touch each other externally. The sum of their areas is (106π)cm2 and the distance between their centers is 14 cm. Find the sum diameters of the circles.
28 cm
Let the radius of bigger and smaller circle be 'R' and 'r' respectively.
Sum of areas =πR2+πr2=π(R2+r2)
According to question, π(R2+r2)=106π
⇒R2+r2=106−−−(I)
Also, R+r=14
⇒R=14−r−−−−(II)
Putting (II) in (I)
(14−r)2+r2=106
196+r2−28r+r2=106
2r2−28r+90=0
r2−14r+45=0
r2−9r−5r+45=0
r(r−9)−5(r−9)=0
(r−5)(r−9)=0
r=9 or r=5
⇒r=9 cm can't be possible because that means R=5 cm which can't be true for our assumption. So, r=5 cm and R=9 cm. Sum of diameters =(10+18) cm=28 cm