Question

Three circles with radii a, b and c touch each other externally. The tangents drawn at their points of contact meet at a point P whose distance from the points of contact is 4. Then (abc)/(a + b + c) is equal to 

(A)  8

(B)  16

(C)  24

(D)  32 

Answer 1

P is equidistant from the sides of  ΔABC and that distance is 4 (Fig.). Therefore, 4 is the inradius of  ΔABC . The semiperimeter s of  ΔABC is given by

(a + b) + (b + c) + (c + a)/2 = a + b + c

Now Δ is given by