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Question
Find the area of the shaded region in the following figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. (Use π = 3.14)
Solution
It is given a triangle ABC is cut from a circle.
`AC=24 cm `
`BC=10 cm`
`"Area of ΔABC=1/2 ACxxBC"`
` = 1/2xx24xx10`
`=120 cm^2`
In ΔABC,
`∠ACB`, Since any angle inscribed in semicircle is always right angle.
By applying Pythagoras theorem,
`AB^2=AC^2+BC^2`
`=24xx24+10xx10`
`=576++100`
`=676 cm^2`
`OA=AB/2`
`=26/2 cm`
`=13 cm`
We know that the area A of circle of radius r is
`A=pi r^2
`Substituting the value of radius r,
`A=3.14xx13xx13`
`= 530.66 cm^2`
Area of semicircle=`1/2 pir^2`
` =530.66/2 cm^2`
` =265.33 cm^2`
`"Area of shadded region=Area of semicircle-Area of triangle" `
`=530.66-265.33-120`
`= 145.33 cm^2`
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