Question

Three circles of radii 3, 4 and 5 units touch each other externally. The tangents drawn at the points of contact are concurrent at point P. If k is the distance of P from the points of contact, then [k] (which is the integer part of k) is .....

Answer 1

Let A, B and C be the centres of the circles with radii 3, 4 and 5, respectively. Hence, the sides of the ΔABC are AB = 7, BC = 9 and CA = 8. Therefore, s = 12 and Δ = √(12 x 3 x 4 x 5) = 12√5 k is the inradius of  ΔABC which is given by

Δ/s = √5

 Therefore, [k] = 2