Question 385197
A central angle intercepts an arc of a circle equal in length to a diameter of
the circle, find the measure of the central angle in radians.
<pre>
By definition, a central angle which intercepts an arc of a circle equal in
length to a radius has a measure of 1 radian.

Since a diameter is twice a radius, a central angle intercepts an arc of a
circle equal in length to a diameter of the circle has a measure of two
radians.

The picture on the left below is a central angle which intercepts an arc of the
circle equal in length to a radius and thus has a measure of 1 radian.

The picture on the right below is your problem. It is a central angle which
intercepts an arc of a circle equal in length to a diameter and thus has a
measure of 2 radians. 

{{{drawing(400,400,-1.2,1.2, -1.2,1.2, locate(.2,.2,1radian),
green(line(0,0,cos(1),sin(1)),line(0,0,1,0), arc(0,0,2,-2,0,180/pi)),
arc(0,0,2,-2,180/pi,360)   )}}}{{{drawing(400,400,-1.2,1.2, -1.2,1.2,
green(line(0,0,cos(2),sin(2)),line(0,0,1,0), arc(0,0,2,-2,0,360/pi)),
arc(0,0,2,-2,360/pi,360),locate(0,.2,2radians)
   )}}}  

The green arc on the left is equal in length to 1 radius, and measures 1 radian.
The green arc on the right is equal in length to 1 diameter, or 2 radii, and
therefore measures 2 radians.

Edwin</pre>