Could you help me with this math question please?

Begoner
Sat, 24 May 2008 23:14:08 +0000

What are you talking about? In your one equation, you have two unknowns: the central angle and the radius. You’re right that you don’t need the central angle, but you’re using the wrong approach. As several people have stated, you must use proportions; knowing that the central angle is the same in both circles, you can deduce that the arc lengths are proportional to the radii.

x / 6 = ( r + 3 ) / r
x = ( 6r + 18 ) / r

The value of x can take on several values; if you doubt it, you can try visualizing it this way. Shrink the smaller circle to half its current size and enlarge the central angle so that the arc length is still 6. Now extend the lines that define the arc by 3 in each direction. Does the length of the second arc change when you apply this transformation? Yes. In fact, the second arc can take on any value in the interval (6, 6 + 6 * pi).