SOLUTION: If a chord 10 inches long is 5 inches from the center of a circle, what is the radius of the circle(sqaure root answer)? In a circle with a 12-inch radius, what is the length of

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Question 272729: If a chord 10 inches long is 5 inches from the center of a circle, what is the radius of the circle(sqaure root answer)?
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)?
What is the radius of a circle in which an inscribed square has a side of 8 inches(square root answer)
Answer by ankor@dixie-net.com(15623) About Me  (Show Source):
You can put this solution on YOUR website!
All these can be solved using pytha: a%5E2+%2B+b%5E2+=+c%5E2 or
c = sqrt%28a%5E2+%2B+b%5E2%29
or
a = sqrt%28c%5E2+-+b%5E2%29
:

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%285%5E2+%2B+5%5E2%29
r = sqrt%2850%29
Factor to reveal a perfect square
r = sqrt%2825%2A2%29
r = 5%2Asqrt%282%29
:
:
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%2812%5E2+-+10%5E2%29
s = sqrt%28144+-+100%29
s = sqrt%28244%29
Factor to reveal a perfect square
r = sqrt%284%2A61%29
r = 2%2Asqrt%2861%29
:
:
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 = %28sqrt%288%5E2%2B8%5E2%29%29%2F2
r = %28sqrt%28128%29%29%2F2
r = %28sqrt%2864%2A2%29%29%2F2
r = %288%2Asqrt%282%29%29%2F2
r = 4%2Asqrt%282%29