CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 4 Marks Questions With Solution 2021
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CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 4 Marks Questions With Solution 2021
10th Standard CBSE

Reg.No. :
Maths

In the given figure, arcs have been drawn with radius 14 cm each and with centres P,Q and R. Find the area of the shaded region.
(a) 
In the given figure, arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.
(a) 
Find the area of the segment of a circle of radius 12 cm, whose corresponding sector has a central angle of 60^{o} . [Take, \(\pi =3.14\)].
(a) 
Four circular cardboard pieces of radius 7 cm are placed on a paper in such a way that each piece touches other two pieces, Find the area of the portion enclosed between these pieces.
(a) 
In the figure given alongside, a circle is inscribed in a square of side 4 ern and another circle is circumscribing the square. Prove that the area of the circumscribed circle is two times the area of the inscribed circle.
(a)
4 Marks
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CBSE 10th Standard Maths Subject Areas Related to Circles Ncert Exemplar 4 Marks Questions With Solution 2021 Answer Keys

308 cm^{2}

1386 cm^{2}

(75.36  \(36\sqrt { 3 } \)) cm^{2}

42 cm^{2}

Let r_{1}=radius of the inscribed circle=\(\frac {4}{2}\)=2 cm
and r_{2}=radius of the circumscribed circle
Now, in triangle OBA,
(OA)^{2}=(OB)^{2}+(BA)^{2}
[by Pythagoras theorem].
\(\Rightarrow \quad { r }^{ 2 }={ r }_{ 1 }^{ 2 }+{ r }_{ 1 }^{ 2 }\)
\(\Rightarrow { r }_{ 2 }=\sqrt { 2{ r }_{ 1 }^{ 2 } } \)
\(\Rightarrow { r }_{ 2 }=\sqrt { 2\times { 2 }^{ 2 } } =2\sqrt { 2 } cm\)
Now, area of inscribed circle
\(=\pi { r }_{ 1 }^{ 2 }=\pi { (2) }^{ 2 }=4\pi \quad { cm }^{ 2 }\) ..(i)
and area of circumscribed circle=\(\pi { r }_{ 2 }^{ 2 }=\pi { (2\sqrt { 2 } ) }^{ 2 }=8\pi \quad { cm }^{ 2 }\)
Area of circumscribed circle=\(2(4\pi )\)
=2 x (Area of inscribed circle) [from Eq. (i)]
4 Marks