From the diagram we see that SP, SR are tangents to circle1 from same point S. Similarly SR, SQ are tangents from same point to circle 2.
SP = SR; SQ = SR implies SP = SQ
Given PQ = 6cm
SP + SQ = 6
Therefor SR = SP = SQ = 3 cm.
SR is the altitude to the triangle SO_{1}O_{2}. We need to find the length of the base O_{1}O2_{2} to determine the area.
O_{1}RS is a right angled triangle with hypotenuse = 5 and one side = 3
Therefore, O_{1}R = = 4 cm
Similarly, O_{2}RS is a right angled triangle with hypotenuse = 4 and one side = 3
Therefore, O_{2}R = = cm
O_{1}O_{2} = O_{1}R + O_{2}R = 4 +
Area of the triangle SO_{1}O_{2} = 1/2 * SR * O_{1}O_{2} = 1/2 * 3 * (4 + ) cm^{2}.
Correct Answer: (B). 3(4 + )/2 cm^{2}