Circles with centers A,B and C touch each other externally. If AB=3cm , BC =3 cm, CA =4 cm , then find the radii of each circle.
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The radii of each circle is 2 cm, 1 cm, and 2 cm respectively.
Step-by-step explanation:
Given Data:
The circles with centers A,B and C and touch with each other externally;
AB=3 cm;
BC=3 cm;
CA=4 cm.
To find: The Radii of the each circle
Let us consider the radii of circle as a, b, and c.
By the definition,the point where two circles touch each other lie on the line joining the centres of the two circles.
By this definition let us consider,
AB = 3 cm
so, a + b = 3 { sum of the two radii} ----->(equation 1)
Similarly,
BC =3 cm
b + c = 3------>(equation 2)
CA = 4 cm
c + a = 4 ------>(equation 3)
By the equation (1) and equation (3) that c=a ;
Substitute the value of 'c' in the equation (3)
a + a = 4
2 a = 4
a = 2
By the equation a = c,
Then, c = 2
And substitute c = 2 in equation (2),
b + 2 = 3
b = 1
So,the radii of each circle is 2 cm,1 cm and 2 cm , when AB = 3 cm, BC = 3 cm, CA = 4 cm.
To Learn More ...
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