`A B C D` is a square of unit area. A circle is tangent to two sides of `A B C D` and passes through exactly one of its vertices. The radius of the circle is `2-sqrt(2)` (b) `sqrt(2)-1` `1//2` (d) `1/(sqrt(2))`

ABCD is a square of unit area.A circle is tangent to two sides of ABCD and passes through exactly one of its vertices.The radius of the circle is:

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the center of the circle lies on x-2y=4. The radius of the circle is 3sqrt(5)(b)5sqrt(3)(c)2sqrt(5)(d)5sqrt(2)

The area of a square is equal to the area of a circle.The ratio between the side of the square and the radius of the circle is (a) sqrt(pi):1 (b) 1:sqrt(pi)(c)1:pi(d)pi:1

Two equal circles of radius r intersect such that each passes through the centre of the other.The length of the common chord of the circles is sqrt(r)(b)sqrt(2)rAB(c)sqrt(3)r(d)(sqrt(3))/(2)r

A circle is circumscribed around a square as shown in the figure.The area of one of the four shaded portions is equal to (4)/(7). The radius of the circle is (FIGURE) sqrt(2)( b) (1)/(sqrt(2))(c)2(d)3

A B C D is a square of side 4 cm. If E is a point in the interior of the square such that C E D is equilateral, then area of A C E is (a) 2(sqrt(3)-1)c m^2 (b) 4(sqrt(3)-1)c m^2 (c) 6(sqrt(3)-1)c m^2 (d) 8(sqrt(3)-1)c m^2

(sqrt8)^(1/3) = ? (a) 2 (b) 4 (c) sqrt2 (d) 2sqrt2

Radius of the circle that passes through the origin and touches the parabola y^(2)=4ax at the point (a,2a) is (a) (5)/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt((5)/(2))a (d) (3)/(sqrt(2))a

(c) 103 (d) 10 18.A circle is inscribed in an equilateral triangle with side lengths 6 unit. Another circle is drawn inside the triangle (but outside the first circle),tangent to the first circle and two of the sides of the triangle.The radius of the smaller circle is (b) 2/3 (a) 1/3 (c) 2 (d) 1

If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is 1+2i, then its perimeter is 2sqrt(5)b.6sqrt(2)c4sqrt(5)d.6sqrt(5)