12/3/24 Sectors, Arcs, Angles, & Tangents

A tangent line is a straight line that touches a curve at a single point without crossing it. In the context of circles, it is perpendicular to the radius at the point of contact.

The length of the tangent segment can be found using the formula: $$\text{Length} = \text{sqrt}(d^2 - r^2)$$ , where $$d$$ is the distance from the point to the center of the circle and $$r$$ is the radius.

The measure of the angle formed by two tangent lines to a circle is equal to half the difference of the measures of the intercepted arcs.

The lengths of the two tangent segments from a point outside the circle to the points of tangency are equal.

The radius drawn to the point of tangency is perpendicular to the tangent line.

To calculate the perimeter, sum the lengths of all sides, including the lengths of the tangent segments.

The measure of the angle is given by the formula: $$\text{Angle} = \frac{1}{2}(\text{larger arc} - \text{smaller arc})$$ .

The measure of the angle formed by a tangent and a chord is equal to the measure of the intercepted arc.

The measure of the angle formed by the two tangents is equal to half the difference of the measures of the arcs that the tangents intercept.

The point of tangency is the point where a tangent line touches the circle, and it is the only point at which the tangent line and the circle meet.