Please can you draw the full construction

I understand you're asking for a visual representation of the construction. As an AI, I am unable to draw diagrams or images directly. However, I can reiterate the steps for you to follow precisely with your geometric tools (ruler, compass, protractor) to create the construction yourself.

Here are the steps again, focusing on the actions you need to take:

a) (i) Construct a triangle PQR such that $|PQ|= 8 \text{ cm}$, $\angle RPQ = 90^\circ$ and $\angle PQR = 30^\circ$. Measure $|RQ|$.

1. Draw Base PQ: Use your ruler to draw a straight line segment $8 \text{ cm}$ long. Label the endpoints P and Q.
2. Construct $90^\circ$ at P: Place the compass point at P. Draw an arc that intersects the line PQ. From that intersection point, draw another arc above PQ. Without changing the compass width, place the compass point at the second intersection on PQ and draw another arc that intersects the first arc you drew above PQ. Draw a straight line from P through this intersection point. This line is perpendicular to PQ.
3. Construct $30^\circ$ at Q: Place the compass point at Q. Draw an arc that intersects the line PQ. From that intersection point, draw another arc of the same radius that intersects the first arc. This creates a $60^\circ$ angle. To bisect this $60^\circ$ angle to get $30^\circ$, place the compass point at the intersection of the arc and PQ, draw an arc. Then, place the compass point at the intersection of the two arcs (the $60^\circ$ mark), and draw another arc that intersects the first. Draw a line from Q through this new intersection point.
4. Locate R: The line from P (the $90^\circ$ line) and the line from Q (the $30^\circ$ line) will intersect. Label this intersection point R. You have now constructed $\triangle PQR$.
5. Measure RQ: Use your ruler to measure the length of the segment from R to Q.

a) (ii) Construct the perpendicular bisector (mediator) of RQ. Let it meet RQ at O.

1. Bisect RQ: Place the compass point at R. Open the compass to a width greater than half the length of RQ. Draw an arc above and below the line segment RQ.
2. Repeat from Q: Without changing the compass width, place the compass point at Q. Draw arcs above and below RQ that intersect the arcs you drew from R.
3. Draw Bisector: Use your ruler to draw a straight line connecting the two points where the arcs intersect. This line is the perpendicular bisector of RQ.
4. Locate O: Label the point where this perpendicular bisector crosses the line segment RQ as O.

b) With O as centre and radius OP, draw a circle. Measure $|OP|$.

1. Set Compass Radius: Place the compass point at O. Adjust the compass opening so the pencil tip is exactly on point P.
2. Draw Circle: Draw a full circle with O as the center and OP as the radius. This circle should pass through points P, Q, and R.
3. Measure OP: Use your ruler to measure the length of the segment from O to P.

c) What is the special name for the chord RQ?

The special name for the chord RQ is the diameter.

I hope these detailed steps help you create the construction accurately! Send me the next one 📸