Question

(1)
Circles with centres A, B and C touch each other externally. If!
AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that radius of three circles be having centres A, B ans C respectively be x, y and z units respectively.

Now,

Given that,

• AB = 3 cm

• BC = 3 cm

• CA = 4 cm

So,

$\rm :\longmapsto\:x + y = 3 - - - (1)$

$\rm :\longmapsto\:y + z = 3 - - - (2)$

$\rm :\longmapsto\:z + x = 4 - - - (3)$

On adding equation (1), (2) and (3), we get

$\rm :\longmapsto\:2(x + y + z) = 10$

$\rm :\longmapsto\:x + y + z= 5 - - - (4)$

On Subtracting equation (1) from (4), we get

$\rm :\longmapsto\:z = 2$

On Subtracting equation (2) from equation (4), we get

$\rm :\longmapsto\:x = 2$

On Subtracting equation (3) from equation (4), we get

$\rm :\longmapsto\:y = 1$

So,

$\purple{\begin{gathered}\begin{gathered}\bf\: Radius \: are-\begin{cases} &\sf{x = 2 \: cm} \\ &\sf{y = 1 \: cm} \\ &\sf{z = 2 \: cm} \end{cases}\end{gathered}\end{gathered}}$

Additional Information :-

1. Length of tangents drawn from external point are equal.

2. Only one tangent can be drawn from a point on circle.

3. A circle can have infinitely many tangents.

4. Radius and tangent are perpendicular to each other.

5. Tangents are equally inclined to the line segment joining the centre and external point.