Question

Three circle of radius 3, 4, 5 touch each other externally. Tangents are drawn at the point of contact, which meet at P. Find the distance between point of contact and P.

Answer 1

PD = PE = PF = r $\frac{S}{s}$
When 2s = 2 (3 + 4 + 5) or s = 12
$S^2$ = s (s - a) (s - b ) (s - c )
= 12 (12 - 7 ) (12 - 9 )(12 - 8 )
= 12 . 5 . 3 . 4
= 12 . 12 . 5
$\therefore S=12\sqrt{5}$
$\therefore r=\frac{S}{s}=\sqrt{5}$=$PD=PE=PF$