Question

In the figure three circles with centers a,b,c respectively touch each other externally if ab= 5cm ,bc=7cm and CA = 6 cm then find radius of tha circle with center a

Answer 1

$\textbf{Given:}$

$\textsf{AB= 5cm, BC=7cm, AC= 6cm}$

$\textbf{To find:}$

$\textsf{Radii of the given circles}$

$\textbf{Solution:}$

$\mathsf{Let\;r_1,r_2\;and\;r_3\;be}\;\textsf{radii of the circles whose centres A,B}$

$\textsf{and C respectively.}$

$\textsf{As per given data, we have}$

$\mathsf{r_1+r_2=5}$........(1)

$\mathsf{r_2+r_3=7}$........(2)

$\mathsf{r_3+r_1=6}$........(3)

$\textsf{Adding (1), (2) and (3)}$

$\mathsf{2(r_1+r_2+r_3)=18}$

$\mathsf{r_1+r_2+r_3=9}$......(4)

$\textsf{Using (1) in (4),}$

$\mathsf{5+r_3=9}$

$\mathsf{r_3=9-5}$

$\implies\boxed{\mathsf{r_3=4}}$

$\textsf{(2) gives,}$

$\mathsf{r_2+4=7}$

$\mathsf{r_2=7-4}$

$\implies\boxed{\mathsf{r_2=3}}$

$\textsf{(1) gives,}$

$\mathsf{r_1+3=5}$

$\mathsf{r_1=5-3}$

$\implies\boxed{\mathsf{r_1=2}}$

$\textbf{Answer:}$

$\textsf{Radii of the given 3 circles are 2cm, 3cm and 4cm}$

$\textbf{Find more:}$

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.​

https://brainly.in/question/15880653

Answer 2

Ur answer is is is

two (2) cm