Question

circles with centre A,B,C touch each other externally if AB= 3 cm,BC= 3cm,CA=4cm then find the radii of each circle​

Answer 1

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

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

$\textbf{Given: AB=3 cm, BC= 3 cm and AC=4 cm}$ 

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

$AB=3\implies\,r_1+r_2=3$...(1)

$BC=3\implies\,r_2+r_3=3$...(2)

$AC=4\implies\,r_1+r_3=4$...(3)

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

$2(r_1+r_2+r_3)=10$

$\implies\,r_1+r_2+r_3=5$...(4)

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

$\implies\,3+r_3=5$

$\implies\,r_3=5-3$

$\implies\boxed{\bf\,r_3=2}$

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

$\implies\,r_1+3=5$

$\implies\,r_1=5-3$

$\implies\boxed{\bf\,r_1=2}$

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

$\implies\,4+r_2=5$

$\implies\,r_2=5-4$

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

$\therefore\textbf{The radii of the given circles are 2cm, 1cm and 2cm}$

Find more:

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.​

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