Three mutually tangent circles of equal radius 2, are shown in the figure. The area of the shaded portion between the three circle is??

Question

Three mutually tangent circles of equal radius 2, are shown in the
figure The area of the shaded portion between the three circle
is??

Ashwini Kumar · Accepted Answer

P, Q and R are centres of three circles
Join P-Q, Q-R and R-PNow,PQR is equilateral triangle, whose side is 4 cm
Area of △PQR=3442=43 cm2Now, each angle of triangle=60°Area of sector of each triangle=60360×π×r2=16×227×22=4421 cm2Area of sector of all three triangles=3×4421=447 cm2Area of required region=43 -447=4×1
732-6 285=6 928-6 285=0 643 cm2