# circles of radii 5,5,8 touch each other externally.Find the radius of the circle which touches all the three circles internally.

Deepak Bohra
33 Points
9 years ago
9 years ago
?
71 Points
9 years ago
Abhishek Singh
105 Points
9 years ago
r=8/9
sarim khan
4 Points
9 years ago
@ abhishek singh ..that is the easy one . it is for externally that u r telling .. the question reads internally my frnd.
Abhishek Singh
105 Points
9 years ago
if you draw yhe diagram, and put C1,C2 the centre of circle with r=5.
c3 the centre of circle of r=3.
Since circle(c3) touch the both circle C3C1=C3C1 -->C3 lies on perp. bisector of C1C2.
let y3 be dist. of c3 from line c1c2. we get 132=y32+52. --->y=12
Similarly for circle(radius of whom is to be known)(centre c4)(similarly C4 lies on.....)(radius r)
let y4 be dist. of c3 from line c1c2.(5+r)2=y42+52.
For touching of Circles(C3 andC4). 8+r=y3-y4             (dist between centre= sum of radii)
substituting value of y3 and y4 in eqn. and solve for r, we get r=8/9