Three circles touch each other externally . A triangle is formed when the centre s of these circles are joined together . Find the radii of the circles, if the sides of the triangle formed are 6 cm , 8 cm and 9 cm

Open in App

Solution

Let ABC be the triangle formed when centres of 3 circles are joined .
Given ,
AB = 6 cm , AC = 8 cm and BC = 9 cm
And let the radii of the circles having centers A,B and C be $r_{1}, r_{2} a n d r_{30}$ respectively .
So, we have
$r_{1} + r_{3} = 8$
$r_{3} + r_{2} = 9$
$r_{2} + r_{1} = 6$
Adding all the above equations, we get
$r_{1} + r_{3} + r_{3} + r_{2} + r_{2} + r_{1} = 8 + 9 + 62 (r_{1} + r_{2} + r_{3}) = 23$
So,
$r_{1}, + r_{2} + r_{3} = 11.5 c m$
Now,
$r_{1} + 9 = 11.5 (A s r_{2} + r_{3} = 9)$
$r_{1} = 2.5 c m$
And,
$r_{2} + 6 = 11.5 (A s r_{1} + r_{2} = 6)$
$r_{2} = 5.5 c m$
Lastly $r_{3} + 8 = 11.5 (A s r_{2} + r_{1} = 8)$
$r_{3} = 3.5 c m$
Therefore , the radii of circles are $r_{1} = 5.5 c m$ and $r_{3} = 3.5 c m$

Suggest Corrections

Similar questions

Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circles, if the sides fo the triangle formed are 6 cm, 8 cm and 9 cm.

Three circles touch each other externally. A triangle is formed when the centers of these circles are joined together. Find the sum of the radii of the three circles, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

Q. Three circles touch each other externally. Find the radii of the circles if the sides of the triangle formed by joining the centres are 7 cm, 8 cm and 9 cm respectively.

Q. Three circles touch each other each other externally. Find the radii of the circles if the sides of the triangle obtained by joining the centres are 10 cm, 14 cm and 16 cm respectively.

Q. Three circles are described touching each other at two places externally. If the sides of triangle are

4 c m, 6 c m

and

8 c m

.Find the radii of the circles.

Join BYJU'S Learning Program