Tangent to a circle
- A tangent line to a circle is a line that touches the circle at exactly one point.
- A tangent to a circle is perpendicular to the radius at the point of tangency.
Theorem 1 : The tangent of a circle is perpendicular
If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.
Theorem 2: Two tangents Theorem
If two tangents are drawn to a circle from an exterior point (the points which lies outside the circle):
- The tangents are equal in length
- The tangent subtend equal angles at the center of the circle and
- The tangents are equally inclined to the line joining the point and the center of the circle.
Theorem : 3
Intersecting Chords Theorem 1
If two chords of a circle intersect internally or externally, then the product of the lengths of their segments is equal.
- For the chords intersecting internally, EA EB = EC ED
- For the chords intersecting externally, EA EB = EC ED
Theorem 2(Alternate segment theorem)
The angle between a tangent and a chord through the point of contact is equal to an angle in the alternate segment.
- PTS = SRT
- PTU = UST
If a chord and a tangent intersect externally, then the product of the lengths of the segment of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.