Angle in a Semicircle Flashcards

All 4 cards in this deck

State the circle theorem about the angle in a semicircle.

The angle in a semicircle is $90^\circ$ (the angle at the circumference subtended by a diameter is a right angle).

The angle in a semicircle being $90^\circ$ is a special case of which circle theorem?

The angle at the centre is twice the angle at the circumference — the angle at the centre is a straight line, $180^\circ$, so the angle at the circumference is $90^\circ$.

What must you check before using the 'angle in a semicircle' theorem?

That the side opposite the angle is a diameter, i.e. it passes through the centre.

True or false? In a triangle drawn in a semicircle, the right angle is the one at the centre.

False. The right angle is at the vertex on the circumference, opposite the diameter.