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प्रश्न
The area of the circle that can be inscribed in a square of side 10 cm is
विकल्प
40 π cm2
30 π cm2
100 π cm2
25 π cm2
उत्तर
We know that ABCD is a square of length 10 cm. A circle is inscribed in the square therefore, all the sides of the square are become tangents of the circle.
By, the tangent property, we have
`AP=PD=5`
`AQ=QB=5`
`BR=RC=5`
`CS+DS=5`
If we join PR then it will be the diameter of the circle of 10 cm.
Therefore, radius of the circle = 5cm
∴ Area of the circle=`pir^2`
∴ Area of the circle=`pixx5^2`
∴ Area of the circle=`25pi`
Therefore, area of the circle is `25picm^2`
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