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

Hey mate! Here's your answer.

Radius of circle with Centre A is 2 cm

Radius of circle with Centre b is is 1 cm

Radius of circle with Centre C is 2 cm

Answer 2

The radii of the circles with centers A,B and C be 2 cm, 1 cm, and 2 cm respectively.

Explanation:

Let the radii of the circles with centers A,B and C be r1, r2 and r3 respectively.

The point where two circles touch each other lie on the line joining the centers of the two circles.

It is given that AB=3 cm, CA=4 cm and BC=3 cm.

$\text{r}_1+\text{r}_2=3 -----> (1)$

$\text{r}_1+ \text{r}_3=4 -----> (2)$

$\text{r}_2+ \text{r}_3=3 ----> (3)$

From the equations (1) and (3), we get,

$\text{r}_1 = \text{r}_3$

Substitute the above relation in equation (2)

we get,

$\text{r}_1+ \text{r}_1 =4$

$2\text{r}_1 =4$

$\text{r}_1 =2$

Then, $\text{r}_3 = 2$

Substitute the respective value in equation (1)

$2+\text{r}_2=3$

$\text{r}_2=3 - 2$

$\text{r}_2 = 1$

Therefore,The radii of the circles with centers A, B and C be 2 cm, 1 cm, and 2 cm respectively.

 

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