(a) A chord is subtending an angle of 90∘ at the centre of a circle of radius 14 cm. Find the area of the corresponding minor segment of the circle.
OR
(b) Find the area of the shaded region if length of radius of each circle is 7 cm. Each circle touches the other two externally.
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Step-by-Step Solution
Step 1: Identify given values
We are given the radius of the circle, r=14 cm, and the angle subtended by the chord at the center, θ=90∘. This angle is for the sector.
Step 2: Calculate the area of the sector
The area of a sector with angle θ and radius r is given by the formula 360∘θ×πr2. Substituting the given values, we can calculate the area of the sector.
Step 3: Calculate the area of the triangle
The area of the triangle formed by the two radii and the chord can be calculated using the formula 21r2sinθ. Since θ=90∘, sin(90∘)=1.
Step 4: Calculate the area of the minor segment
The area of the minor segment is the difference between the area of the sector and the area of the triangle. We subtract the calculated area of the triangle from the area of the sector to get the final answer.