Question 38210: two parallel chords, 16 cm and 30 cm are 23 cm apart. find the radius of the circle that contains them.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Oooh, good problem.
Here's how you do it...
Make yourself the diagram with the parallel chords, one on either side of the center. Be sure that the 23 cm line that joins the two chords bisects them both.
That line goes thru the center.
Now draw two radii to the ends of the chords so that two right triangles are formed.
Label the distance from the center to the 30 cm chord, x.
Thus the distance from the center to the 16 cm is 23 - x.
Now you have two Pythagorean Theorems to write:
8^2 + (23 - x)^2 = r^2 and
15^2 + x^2 = r^2
Two equations, two unknowns...we can solve this...here goes...
8^2 + (23 - x)^2 = 15^2 + x^2
64 + 529 - 46x + x^2 = 225 + x^2
-46x + 593 = 225
-46x = -368
x = 8
Thus r^2 = 15^2 + 8^2 and voila,
r = 17
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