Circles are drawn from 3 vertices of a triangle ABC taken as centre to touch each other externally. the sides of the triangle are 4cm, 6cm, 8cm. find the radii of the circles

 Hi!

Here is the answer to your query.

 

Given : AB = 4 cm

BC = 6 cm

AC = 8 cm

Let the circle with centre A, intersects AB and AC at D and F respectively.

∴ AD = AF = x (radius)

 Similarly BD = BE = y (radius)

and CE = CF = z (radius)

 

Now, AB = AD + BD = 4 cm

⇒ x + y = 4    ......(1)

BC = BE + CE = 6 cm

⇒ y + z = 6    .......(2)

AC = AF + CF = 8 cm

⇒ x + z = 8    ......(3)

 

Add equation (1), (2) and (3), we have

2 (x + y + z) = 4 + 6 + 8

⇒ x + y + z = 9    ..... (4)

 

solves equation (1) and (4), we get

z = 5 cm

from equation (2) and (4), we get

x = 3 cm

from equation (3) and (4), we get

y = 1 cm

 

Hence, radius of circle with centre A = x = 3 cm

Hence, radius of circle with centre B = y = 1 cm

and Hence, radius of circle with centre C = z = 5 cm

 

Cheers!