Question

If three circles touch externally with centre A, B, C and AB = 4 cm BC =6 cm andCA= 8 cm then find the radii of the circles.​

Answer 1

$\text{Let r_1,r_2 and r_3 be radii of the circles having}$

$\text{centres A,B and C respectively}$

$\textbf{Given: AB=4 cm, BC= 6 cm and AC=8 cm}$ 

$\text{From the figure, we have}$

$AB=4\implies\,r_1+r_2=4$...(1)

$BC=6\implies\,r_2+r_3=6$...(2)

$AC=8\implies\,r_1+r_3=8$...(3)

$\text{Adding (1),(2) and (3), we get}$

$2(r_1+r_2+r_3)=18$

$\implies\,r_1+r_2+r_3=9$...(4)

$\text{Using (1) in (4), we get}$

$\implies\,4+r_3=9$

$\implies\,r_3=9-4$

$\implies\boxed{\bf\,r_3=5}$

$\text{Using (2) in (4), we get}$

$\implies\,r_1+6=9$

$\implies\,r_1=9-6$

$\implies\boxed{\bf\,r_1=3}$

$\text{Using (3) in (4), we get}$

$\implies\,8+r_2=9$

$\implies\,r_2=9-8$

$\implies\boxed{\bf\,r_2=1}$

$\therefore\textbf{The radii of the given circles are 3cm, 1cm and 5cm}$

Find more:

Circles with centre A ,B ,C touch each other externally .If AB =3, BC =3, CA =4 ;

then find the radii of each circles

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