Question
AB is the diameter of a circle.
C is a point on AB such that AC = 4cm.
(a) Using a straight edge and compasses only, construct
(i) the locus of points which are equidistant from A and from B,
Answer/Explanation
Ans: 
(ii) the locus of points which are 4 cm from C.
Answer/Explanation
Ans:
(b) Shade the region in the diagram which is
• nearer to B than to A
and
• less than 4 cm from C.
Answer/Explanation
Ans:
Question
In triangle ABC, CN is the bisector of angle ACB.
(a) Using a ruler and compasses only, construct the locus of points inside triangle ABC that are 5.7 cm from B.
Answer/Explanation
Ans: Correct arc centre B, radius 5.7
(b) Shade the region inside triangle ABC that is
• more than 5.7cm from B
and
• nearer to BC than to AC.
Answer/Explanation
Ans: Shading below CN outside arc
Question
(a) The point C lies on AD and angle ABC = 67°.
Draw accurately the line BC.
Answer/Explanation
Ans: angle of 67° at B
(b) Using a straight edge and compasses only, construct the perpendicular bisector of AB.
Show clearly all your construction arcs.
Answer/Explanation
Ans: perpendicular bisector of AB
Question
(a) In this part, use a straight edge and compasses only and show your construction arcs.
Construct accurately
(i) the bisector of angle B,
(ii) the locus of points equidistant from B and from C.
(b) Shade the region inside triangle ABC containing the points which are
nearer to BC than to BA and nearer to C than to B.
Answer/Explanation
Ans:
(a) (i) Accurate bisector of angle B with
correct arcs
(ii) Accurate perpendicular bisector of
BC with correct arcs
(b) correct region shaded
Question
(a) Using compasses and straight edge only, construct
(i) the perpendicular bisector of AC,
Answer/Explanation
Ans: 
(ii) the bisector of angle ACB.
Answer/Explanation
Ans:
(b) Shade the region inside the triangle which is
● nearer to A than to C
and
● nearer to AC than to BC.
Answer/Explanation
Ans:
Question
The line AB is one side of an equilateral triangle ABC.
Using a straight edge and compasses only, construct triangle ABC.
Answer/Explanation
Ans:
Equilateral triangle with correct
arcs
Question
In this question, use a straight edge and compasses only and show all your construction arcs.
(a) Construct the perpendicular bisector of PQ.
(b) Construct the bisector of angle ABC.
Answer/Explanation
(a)Correct ruled perpendicular bisector of AB with correct pairs of arcs
(b)Correct ruled bisectopr of angle ABC with 2 correct pairs of arcs
Question
The diagram shows a triangle ABC and an arc with centre C and radius 6.5cm.
(a) Using a straight edge and compasses only, construct the locus of points inside the triangle that are
equidistant from BA and BC.
(b) Shade the region inside the triangle that is
• more than 6.5cm from C
and
• nearer to BA than to BC.
Answer/Explanation
(a) Correct angle bisector at B with two pairs of correct arcs reaching AC
(b) Correct region shaded
Question
A field, ABC, is in the shape of a triangle.
AC = 500m and BC = 650m.
Using a ruler and compasses only, complete the scale drawing of the field ABC.
Leave in your construction arcs.
Use a scale of 1 cm to represent 100m.
The side AB has been drawn for you.
Answer/Explanation
Correct triangle constructed with
AC = 5 cm and BC = 6.5 cm and
intersecting arcs
Question
Using a ruler and compasses only, construct this triangle. Leave in your construction arcs.
The side of length 12cm has been drawn for you.
Answer/Explanation
correct triangle with arcs
Question
Measure the marked angle.
Answer/Explanation
40°
Question
The point A lies on the circle centre O, radius 5cm.
(a) Using a straight edge and compasses only, construct the perpendicular bisector of the line OA.
(b) The perpendicular bisector meets the circle at the points C and D.
Measure and write down the size of the angle AOD.
Answer/Explanation
(b) 60 degrees
Question
(a) Using a straight edge and compasses only, construct the perpendicular bisector of $A B$ on the diagram above.
(b) Write down the co-ordinates of the midpoint of the line segment joining $A(1,8)$ to $B(7,-4)$.
(c) Find the equation of the line AB.
▶️Answer/Explanation
(a) Bisector
(b) (4, 2)
(c) y = –2x + 10 oe
Question
16 Using a straight edge and compasses only, draw the locus of all points inside the quadrilateral $A B C D$ which are equidistant from the lines $A C$ and $B D$.
Show clearly all your construction arcs.
▶️Answer/Explanation
Angle bisector of angle in the middle Second angle bisector drawn