Angle Measurement

Can someone help me in this problem? I try it but I cannot get the right answer


Three circles with radius 1,2, and 3 ft are extremely tangent to one another. Find the area of the sector of the circle of radius 1 that is cut off by the line segments
joining the center of that circle to the centers of the other two circles.



I think this is the figure of that one

let centre of circle with radius 1 ft= A
let centre of circle with radius 2 ft= B
let centre of circle with radius 3 ft= c
join ABC
so AB=3 ft,BC=5ft,CA=4 ft
it clearly shows that ABC is a right angle triangle with angle CAB=90 degrees.
now we may calculate area of sector of circle with centre A
since angle A is 90 degrees therefor
area of sector = (1/4) area of circle
=(1/4)(pi (1)^2)
=pi/4 square ft