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Question
In the given figure, A is the center of the circle. ∠ABC = 45° and AC = 7√2 cm. Find the area of segment BXC.
Solution
Given Data:
- A is the center of the circle.
- ∠ABC = 45°
- AC = 7√2 cm (This is the radius of the circle as A is the center)
Since AC is the radius, we have: `r = 7sqrt2 cm`
The area of a sector with angle θ in a circle of radius r is given by:
Area of sector = `theta/(360°) xx pir^2`
Area of sector = `90/360xx pi(7sqrt2)^2`
`= 1/4xxpixx98`
`=(98pi)/4 = 24.5pi cm^2`
Area of triangle `= 1/2xx"Base"xx"Height"`
Area of triangle `1/2xx7xx7`
`49/2 = 24.5 cm^2`
Find the Area of the Segment BXC
Area of segment BXC = Area of sector ABC − Area of triangle ABC
= 24.5π − 24.5
= 24.5 (π − 1) cm2
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