Circles with radii 3, 4 and 5 touch each other externally. If P is the point of intersection of tangents to these circles at their points of contact, then if the distance of P from the points of contact is `lambda` then `lambda_2` is _____

Answer

5

Explanation

Indeed the required length will be in radius of the triangle
`C_(1) C_(2) C_(3)` whose sides are `3 + 4, 4 + 5, 5 + 3`
Use `r = (Delta)/(s)` to get distance `sqrt(5) rArr lambda = 5`