Circle angles, chords and tangents

The two tangent segments drawn to a circle from the same external point are equal.

If the external point is P and the points of tangency are T and S, then:

PT = PS.

Therefore, the second tangent segment has the same length as the given first segment. No additional calculation is required.

A central angle intercepting the same arc as an inscribed angle is twice as large:

central angle = 2 · inscribed angle.

Multiply the given inscribed angle by 2. The resulting angle cannot exceed 360°.

A central angle and an inscribed angle intercept the same arc. Their measures are related by:

inscribed angle = central angle / 2.

Divide the given central angle by 2. Before calculating, make sure that both angles really intercept the same arc.

A tangent is a line that has exactly one common point with a circle. This point is called the point of tangency.

A radius drawn from the centre to the point of tangency is always perpendicular to the tangent. Therefore, the angle between them is a right angle.

The two tangent segments drawn to a circle from the same external point are equal.

If the external point is P and the points of tangency are T and S, then:

PT = PS.

Therefore, the second tangent segment has the same length as the given first segment. No additional calculation is required.