the area of a square inscribed in a circle of radius 8cm:

a) 64 b)100 c)125 d)128

if the points (0,0),(1,2) and (x,y) are collinear,then

a)x=y b)2x=y c)x=2y d)2x=-y

Question

the area of a square inscribed in a circle of radius 8cm:
a) 64 b)100 c)125 d)128
if the points (0,0),(1,2) and (x,y) are collinear,then
a)x=y b)2x=y c)x=2y d)2x=-y

Ajanta Trivedi · Accepted Answer

given ABCD is a square, which is inscribed in a circle of radius 8 cm.

since the diagonals of the square subtends right angle at circumference,

therefore the diagonals of square are the diameters of the circle.

BD=2*8=16 cm

let the sides of the square be x cm.

in the right angled triangle BCD,

$B C^{2} + C D^{2} = B D^{2} x^{2} + x^{2} = 16^{2} 2 x^{2} = 256 x^{2} = 128$

thus the area of the square is $x^{2} = 128 c m^{2}$

(2) the given points are (0,0),(1,2) and (x,y) .

if three points $(x_{1}, y_{1}), (x_{2}, y_{2}) a n d (x_{3}, y_{3})$ are collinear.

then $x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) = 0$

$0 (2 - y) + 1 (y - 0) + x (0 - 2) = 0 \Rightarrow 0 + y - 2 x = 0 \Rightarrow 2 x = y$

the area of a square inscribed in a circle of radius 8cm: a) 64 b)100 c)125 d)128 if the points (0,0),(1,2) and (x,y) are collinear,then a)x=y b)2x=y c)x=2y d)2x=-y

the area of a square inscribed in a circle of radius 8cm:

a) 64 b)100 c)125 d)128

if the points (0,0),(1,2) and (x,y) are collinear,then

a)x=y b)2x=y c)x=2y d)2x=-y