The Alternate Segment Theorem Flashcards

All 5 cards in this deck

State the alternate segment theorem.

The angle between a tangent and a chord equals the angle in the alternate segment.

What two features must a diagram have before you can use the alternate segment theorem?

A tangent, and a chord drawn from the point of contact.

Which angle equals the angle between the tangent and the chord?

e.g. tangent $DAE$ at $A$, chord $AB$, $\angle BAE = 56^\circ$, with $C$ on the other side of $AB$

$\angle ACB = 56^\circ$ — the angle in the alternate segment.

True or false? The angle between a tangent and a chord equals the angle in the segment on the same side of the chord.

False. It equals the angle in the alternate (opposite) segment.

True or false? The alternate segment theorem only works if the chord passes through the centre.

False. It works for any chord drawn from the point of contact.