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.

Circles

• $(x - h)^2 + (y - k)^2 = r^2$: center $(h, k)$, radius $r$.
• Expanded form: complete the square in $x$ and in $y$.

Watch out: $(x + 3)$ means $h = -3$, and the right side is $r^2$.

Parabolas

• $x^2 = 4py$: focus $(0, p)$, directrix $y = -p$.
• $y^2 = 4px$: focus $(p, 0)$, directrix $x = -p$.

Watch out: divide by 4 to get $p$.

Partitioning a segment

$A + t(B - A)$; ratio $m : n$ gives $t = \dfrac{m}{m + n}$.

Watch out: count the parts of the ratio.