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two circles touch Each Other externally the sum of the areas is 149 Pi cm and the distance between the centres is 17 cm find the radius of the circle
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[tex]\huge\fbox\pink{good morning}[/tex]
two circles touch Each Other externally the sum of the areas is 149 Pi cm and the distance between the centres is 17 cm find the radius of the circle
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Let the radius of the two circles are a and b cm
The circles touch each other externally.
So, the distance between their centers =a+b
a+b=14 ................... (1)
Sum of their areas =πa² +πb²
πa² +πb² =130π
a² +b² =130 .................... (2)
From equation (1),
b=14−a ............. (3)
From (2) and (3),
a² +(14−a) ² =130
a² +a² +196−28a=130
2a² +66−28a=0a² +33−14a=0a² −11a−3a+33=0
(a−11)(a−3)=0
a=3,11
If a=3, then b=14−3=11
If a=11, then b=14−11=3
So, the radius of the two circles are 3 and 11 cm
And their diameters are 6 and 22 cm.