Summary
Highlights
A tangent line is a line that intersects a circle at exactly one point, known as the point of tangency. This section explains the definition and illustrates it with an example where line CD is tangent to a circle at point B. A postulate states that through any given point on a circle, only one tangent line can be drawn.
Three theorems regarding tangent lines are discussed: 1) A tangent line is perpendicular to the radius drawn to the point of tangency. 2) If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. 3) If two segments from the same exterior point are tangent to a circle, then the two segments are congruent.
A common tangent is a line tangent to two circles in the same plane. There are two types: common internal tangents, which intersect the segment joining the centers of the two circles, and common external tangents, which do not.
A secant is a line that intersects a circle at exactly two points. This differentiates it from a tangent line, which only intersects at one point. A chord is a segment of a secant line.
If two secants intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. An example is provided where angle CAE is calculated using the difference of arc CE and arc BD.
If a secant and a tangent intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. An example demonstrates calculating angle APD using arc AD and arc AB.
If two tangents intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. The calculation of angle PMR is shown using arc RPQ and arc RPR.
If two secants intersect in the interior of a circle, the measure of the angle formed is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Examples illustrate how to find angle 1 and angle 2 using intercepted arcs.
If a secant and a tangent intersect at the point of tangency, the measure of each angle formed is half the measure of its intercepted arc. The video provides examples for calculating angle NJk and angle MGK based on their respective intercepted arcs.