pythagoras theorem - finding a radius of a circle within a rectangle.... PLZ HELP?

Question

a circle passes through opposite vetices of a square with side 40cm. If the diagonal of the square is a diameter of the circle, calculate the radius of the circle

Answer 1

We have a square with side 40cm, and the diagonal of the square is a diameter of the circle.



First we need to find the diagonal of the square, which is the hypotenuse of a triangle with the other two sides 40cm. Pythagoras' theorem tells us that the diagonal is the square root of the sum of the squares of the other two sides:



Diagonal = sqrt(40^2 + 40^2) = sqrt(1600 + 1600) = sqrt(3200) = 56.568542



The radius of the circle is simply half the diameter, that is 28.284271 cm

Answer 2

Find the lengths of 2 sides of the rectangle.



Square them.

Add them together.

Find the square root of that.

You have the diameter of the circle.

To get radius divide diameter by 2.



Eg. Side 1= 4 Side 2=3

a^2+b^2=c^2

4^2+3^2=

16+9=25

c=sqrt (25)

c=5

d=5

Answer 3

Ignore the circle, and look at the square, 40 on a side...what is the length of that circles' diagonal? Half that, and you have the radius you seek.

Answer 4

easy.....the 2 sides of the square n the diagonal make a rite angld triangle n u can find the length of the diagonal of the squae by applying pythagorus theorm....then v knw dat the diagonal happns 2 b the diameter n radius is half the diameter...so

diiagonal=diameter=1/2(radius)....

wen v apply pythagorus...the diagonal cums out 2 b 40*square root of 2

n therfore radius+20*square root of 2!!!1

did u get it??

Answer 5

Pythagorean theorem you advise? i'm not sure how old you're, so i will't anticipate the type you will understand. the respond is confident. ideally, there are 2 common approaches to graph a function, utilising Polar Coordinates, and Cartesian Coordinates. With Cartesian coordinates it could look like the only use for Pythagorean's Theorem is for planar action, yet while changing to Polar Coordinates the assumption is rather diverse. different than for the different a hundred's of situations you will use Pythagorean's Theorem in Polar Coordinate math, that's based on the theory of circles; to transform from Cartesian coordinates to Polar coordinates you desire an x=rcos(theta), and a y=rsin(theta) the place, utilising none different than Pythagorean's Theorem and elementary trigonometry, r = (sqr_root_of:((x^2) + (y^2))) which simplifies out to r^2 = (x^2) + (y^2) Polar coordinates are used in distinctive submit secondary, first and 2nd 12 months algebra training. in case you have not gotten there yet and are nevertheless involved, i might advise you do take those training once you get the possibility. there is so plenty greater to learn with regards to what i've got temporarily touched on. i desire that develop into legible to you and helped!

Answer 6

Side of square = 40 cm

Diagonal of square is Square root of 2*Side*side=

root of 2*40*40=56.56cm



Diameter of circle= 56.56cm

Radius of circle = Diameter/2= 56.56/2=28.28cm



ANSWER 28.28cm