 Interactive Graphical Circle

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Interactive circle with sector and segment

Move the points in the grafic or define the point coordinates in the numeric field.

The radius r is the distance from the center of the circle to the circle circumference. A circle is defined by the set of all points that have the distance r to a point.

Circle circumference

$U=2\pi r$

Circle area

$F=\pi {r}^{2}$

Secant

The chord or secant connects two points of the circle circumference. The length of the secant s is:

$s=2r\mathrm{sin}\left(\frac{\alpha }{2}\right)=2\sqrt{2hr-{h}^{2}}$

with the opening angle α of the sector uand the height h of the circular section.

Arc length

The arc length l of the circle segment is:

$l=\frac{2\pi r\alpha }{360}$

Sector area

The area S of the circle sector is:

$S=\frac{\pi {r}^{2}\alpha }{360}$

Area of the circular section

The circular section is the area between the secant and the circle circumference. The area Sa of the circular section is:

${S}_{a}=\frac{{r}^{2}\left(\frac{\pi \alpha }{180}-\mathrm{sin}\alpha \right)}{2}$

Height of the circular section

The height ha of the circular section is:

${h}_{a}=r-\sqrt{{r}^{2}-\frac{{a}^{2}}{4}}$