WOLFRAM|DEMONSTRATIONS PROJECT

Ratio of the Areas of a Circular Segment and a Curvilinear Triangle

​
distance from center, a
1.815
​
central angle
=
1.97455
radians
​
area of red segment
=
0.527482
sq. units
​
area of blue
curvilinear triangle
=
0.527393
sq. units
​
blue area / red area
=
0.999832
Two tangent lines are drawn from a point
P(a,0)
to the unit circle with center
(0,0)
radius 1. The limit of the ratio
B/A
between the blue area
B
between the two tangent lines and the circle to the red area
A
of the circular segment as the central angle approaches zero is 1/2. By moving the slider, you can see the changes in this ratio.