What is the angle formed by a tangent and a chord?

The angle formed by a tangent and a chord is equal to the angle in the alternate segment.

When a tangent touches a circle at a point and a chord is drawn from that point, the angle between the tangent and the chord is known as the angle between the tangent and the chord. This angle is equal to the angle in the alternate segment of the circle. The alternate segment is the region of the circle that lies opposite the chord.

To understand this better, imagine a circle with a tangent touching it at point A. Now, draw a chord AB from point A to another point B on the circle. The angle between the tangent at A and the chord AB is equal to the angle in the alternate segment, which is the angle subtended by the chord AB at the circumference of the circle on the opposite side of the chord.

This property is a result of the Alternate Segment Theorem, which states that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. This theorem is very useful in solving various problems related to circles, especially when you need to find unknown angles.

For example, if you know the angle between the tangent and the chord, you can easily find the angle in the alternate segment, and vice versa. This relationship helps in analysing and solving geometric problems involving circles, tangents, and chords more efficiently.