SOLUTION: If AB and CD are the two chords of a circle such that AB=6cm and CD= 12 cm , AB andCD are parrelel and distance between the two chords is 3cm find the radius of circle.

Question 977267: If AB and CD are the two chords of a circle such that AB=6cm and CD= 12 cm , AB andCD are parrelel and distance between the two chords is 3cm find the radius of circle.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If AB and CD are the two chords of a circle such that AB=6cm and CD= 12 cm ,
AB and CD are parallel and distance between the two chords is 3cm
find the radius of circle.
:
Draw a decent looking diagram of this, both chords on the same side of the center.
label the two chords. Let x = the distance from the center to the 1st chord (12cm)
Draw radii from center to end points of both chords. Draw a line to center to the further chord so it bisects both chords.
You can see two right triangles are formed the half the chords, the line to the center and the radius, which would be the hypotenuse
The pythag equation for each
r^2 = 6^2 + x^2
and
r^2 = 3^2 + (x+3)^2
r^2 = r^2 so we can write it
3^2 + (x+3)^2 = 6^2 + x^2
9 + x^2 + 6x + 9 = 36 + x^2
Subtract x^2 from both sides, add the 9s
6x + 18 = 36
6x = 36 - 18
6x = 18
x = 18/6
x = 3
now we can find r using pyth
r =
r =
r = 6.71 cm is the radius
We can check this in the other triangle
r =
r =
r = 6.71 cm is the radius
:
:
Did this make sense to you? ankor@att.net would like to know.

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