Problem 12
A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum?
Central angle = Angle subtended by an arc of the circle from the center of the circle. Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle.
Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by
The following are short descriptions of the circle shown below.
Tangent - is a line that would pass through one point on the circle. Secant - is a line that would pass through two points on the circle. Chord - is a secant that would terminate on the circle itself. Diameter, d - is a chord that passes through the center of the circle. Radius, r - is one-half of the diameter.
This page will define the following: incenter, circumcenter, orthocenter, centroid, and Euler line.
Incenter
Incenter is the center of the inscribed circle (incircle) of the triangle, it is the point of intersection of the angle bisectors of the triangle.