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Question
In following figure, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). `["Use" pi=22/7]`
Solution
The given information can be diagrammatically represented as follows:
Here, A, B and C are the centres of the circles.
Radius of each circle, r = 3.5 cm
Thus, the measure of each of the sides of ΔABC is 3.5 cm + 3.5 cm = 7 cm.
Since the sides of triangle ABC are of equal lengths, it is an equilateral triangle.
∴ ∠A = ∠B = ∠C = 60°
Area of the shaded region = Area of ΔABC − (sum of areas of sectors APR, BPQ and CQR)
`=sqrt3/4a^2-3xxO//360^@xxpir`
`=1.732/4xx(7"cm")^2-3xx60^@/360^@xx22/7xx3.5"cm"xx3.5"cm"`
`=21.217 "cm"^2-19.25cm^2`
`=1.97"cm"^2`
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