Important properties of a tangent:
Two tangents from the same external point to the same circle will be of equal length.
Tangent Secant Theorem:
If a tangent and a secant are drawn to a circle from an external point, the square of the length of the tangent segment is equal to the product of the lengths of the entire secant segment and its external secant segment
AT$$^2$$ = AS x AU = AP x AQ
Alternate Segment Theorem:
The angle made by a chord with a tangent to one of the ends of the chord is equal to the angle subtended by the chord in the other segment. As shown in the figure, ∠BAT = ∠ACB
Secant-Secant Theorem:
From a point O outside a circle, two secants are drawn such that the first secant cuts the circle at A and B, and the second secant cuts the circle at C and D.Then, OA*OB = OC*OD.
Intersecting Chord Theorem:
Two chords AB and CD are drawn in such a way that they intersect at a point O. Then, AO x OB = CO x OD.
.png)
