Question

6.
Solve the following sub-questions (Any one):
(1) Circles with centres A, B and C touch each other externally. I
AB = 3 cm, BC = 3 em. CA - 4 cm, then find the radii of each circle​

Answer 1

Answer:

1st radius = 2.5cm

2nd radius = 1.5cm

3rd radius = 0.5cm

I am not sure about 3rd radius but first two radii are correct.

Hope it helps you.

please mark it as brainlist.

Answer 2

The radii of the circles with centers A, B and C are 2 cm, 1 cm and 2 cm

Step-by-step explanation:

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

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

AB = $\text{r}_{1} +\text{r}_{2}$ = 3 ........ (1)

BC =  $\text{r}_{2} +\text{r}_{3}$ = 3 ....... (2)

CA = $\text{r}_{1} +\text{r}_{3}$ = 4 cm .......(3)

From (1) and (3) ,we get

$\text{r}_{1} = \text{r}_{3}$

Substituting  $\text{r}_{3}$ in (3) ,we get

$\text{r}_{1} +\text{r}_{1} = 4$

$2\text{r}_{1} =4$

∴ $\text{r}_{1} = \text{r}_{3} = 2$

and $\text{r}_{2} = 1$

Hence the radii of the circles with centers A, B and C are 2 cm, 1 cm and 2 cm.

To Learn More...

1. OA and OB are mutually perpendicular radii of a circle find the area of minor segment if the perimeter of corresponding minor sector is 20 cm

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2. If the angle between two radii of a circle is 130 degree then find the angle between tangents at the end of radii

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