Question 272729
All these can be solved using pytha: {{{a^2 + b^2 = c^2}}} or 
c = {{{sqrt(a^2 + b^2)}}}
or
a = {{{sqrt(c^2 - b^2)}}}
:


If a chord 10 inches long is 5 inches from the center of a circle,
 what is the radius of the circle(square root answer)?
:
A line from the center to the chord, bisects the chord, therefore you have a
 right triangle, two sides = 5", the hypotenuse = the radius
r = {{{sqrt(5^2 + 5^2)}}}
r = {{{sqrt(50)}}}
Factor to reveal a perfect square
r = {{{sqrt(25*2)}}}
r = {{{5*sqrt(2)}}}
:
:
In a circle with a 12-inch radius, what is the length of a segment joining the 
midpoint of a 20-inch chord and the center of the circle(square rootanswer)?
:
A right triangle is formed by half the chord (10) and the hypotenuse, r (12)
and the segment (s)
s = {{{sqrt(12^2 - 10^2)}}}
s = {{{sqrt(144 - 100)}}}
s = {{{sqrt(244)}}}
Factor to reveal a perfect square
r = {{{sqrt(4*61)}}}
r = {{{2*sqrt(61)}}}
:
:
What is the radius of a circle in which an inscribed square has a side of 8 inches (square root answer)
:
The diameter of the circle will = to the diagonal of the square
r = {{{(sqrt(8^2+8^2))/2}}}
r = {{{(sqrt(128))/2}}}
r = {{{(sqrt(64*2))/2}}}
r = {{{(8*sqrt(2))/2}}}
r = {{{4*sqrt(2)}}}