M CUBE: Math-e-Matics by Maheshwari TANGENCY

Theorem: The angles made by a tangent to a circle with a chord drawn from the point of contact are respectively equal to the angles in the alternate segments of the circle. (ALTERNATE SEGMENT THEOREM)

Let EF touch the circle ABC at B, and let BD be a chord drawn from B, the point of contact. Let BA be the diameter through B, and C any point in the arc of the segment which does not contain A. Construction: Join AD, DC, CB.