Question: Construct triangle $ABC$ with $AB = 6$ cm, $AC = 8$ cm and $BC = 10$ cm, using ruler and compasses only. Measure $\angle BAC$.

Step 1. Draw the base: rule $AB = 6$ cm exactly, and label the ends.

Step 2. The third vertex is fixed by two distances, so use two compass arcs:

set the compasses to $8$ cm and draw an arc centred at $A$;

set them to $10$ cm and draw an arc centred at $B$.

Step 3. The arcs cross at $C$ (choose either intersection — the two options are mirror images). Join $AC$ and $BC$ with a ruler.

Step 4. Measure with a protractor:

— as it must be, since $6^2 + 8^2 = 10^2$ makes this a right-angled triangle (a built-in accuracy check for your drawing: within $\pm 1°$ is fine).

⚠ Watch out: Leave every construction arc visible — rubbed-out arcs lose the method marks; the arcs are the working. Compasses, not protractor, fix $C$: measuring angles to place it answers a different question. Label the vertices as the question names them, or the measured angle can't be credited.

Question: In quadrilateral $ABCD$, construct (a) the perpendicular bisector of $AB$, (b) the bisector of angle $BAD$, and (c) mark the point $P$ where they meet. What is special about $P$?

Step 1. (a) Perpendicular bisector of $AB$: compasses open more than half of $AB$; arcs from $A$ and from $B$ above and below the line; rule through the two crossings. Every point on this line is equidistant from $A$ and $B$.

Step 2. (b) Angle bisector at $A$: one arc across both arms of $\angle BAD$; from the two crossing points, two equal arcs into the angle; rule from $A$ through their intersection. Every point on this line is equidistant from the two arms $AB$ and $AD$.

Step 3. (c) Mark $P$ at the intersection of the two constructed lines.

Step 4. $P$ is the one point that is both the same distance from $A$ as from $B$, and the same distance from line $AB$ as from line $AD$ — exactly how exam questions pin down a treasure/mast/well location. A region version ("nearer to $A$ than $B$ and nearer to $AB$ than $AD$") shades between the same two lines.

⚠ Watch out: The two bisectors answer different "equidistant" questions — from two points (perpendicular bisector) vs from two lines (angle bisector). Matching the wrong locus to the wording is the main mark-loser; the arcs must stay visible in both constructions.