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A chord is a segment whose end points lie on a given circle.
In general, a chord is a segment whose end points lie on a given curve.
Note, some people spell this cord,
but
Merriam Webster spells it chord, meaning 3, so I'm going with that.
To find the length of the chord, given its central angle θ, draw a perpendicular from the center of the circle to the chord, creating two congruent right triangles. Each has a base that is half the chord. The base is sin(θ/2)Śr, so double this to get the chord length. A tangent is a line that is tangent to a given circle or curve. The line touches the circle at just one point. |
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Let the line l be tangent to a given circle centered at p, and let q be the point of tangency. Draw the radius from p to q, and suppose this segment is not perpendicular to l. It is slightly off, say 89°. Draw another radius 2° from the first. These two segments form the equal sides of an isosceles triangle, with base angles of 89°. The base of this isosceles triangle is a chord, and is also part of l. This is a contradiction, hence the tangent line through q is always perpendicular to the radius from p to q. There can be only one tangent line through q.