Revision sheet

Inscribed angles

Inscribed = ½ central; on a diameter: 90°.

Watch out: halve, do not double.

Tangent lines

Tangent ⊥ radius; tangent segments from a point are equal.

Watch out: a right triangle, not a subtraction.

Cyclic quadrilaterals

Opposite angles add to $180^\circ$.

Watch out: supplementary, not equal.

Arcs and sectors

Arc $= \tfrac{\theta}{360} 2\pi r$, sector $= \tfrac{\theta}{360}\pi r^2$.

Watch out: circumference for arcs, area for sectors.

Radians

• $180^\circ = \pi$ rad.
• Degrees → radians: $\times \dfrac{\pi}{180}$. Radians → degrees: $\times \dfrac{180}{\pi}$.
• Arc length: $s = r\theta$, $\theta$ in radians.

Watch out: never put degrees into $s = r\theta$.