The diagram shows the part of the two houses X and Y and a path P.
Scale 1 cm represents 25 m. A public phone is installed such that it is:
• Less than 125 m from X
• Nearer to Y than X
• More than 100 m from the path
Using ruler and compasses only, find the region where the public phone can be placed. Label it T.

The diagram shows triangle RST. (a) Measure and write the size of angle RST.

(b) Q is the point where the angle bisectors of R, S and T meet. Mark and label the position of the point Q.

(c)(i) M is the mid-point of TR and N is the mid-point of RS. Measure the distance, x cm, of line MN from Q.

(ii) Shade the region that is:
• less than x cm from Q,
• nearer to TR than to TS, and
• nearer to RT than to RS.

Triangle ABC is such that AB = 8 cm, AC = 5 cm and angle BAC = 60°.
AB has already been drawn for you. (a) Construct triangle ABC.

(b) Construct the bisector of angle ABC.

(c) Write down the length of BC.

The diagram shows a plan of a triangular plot ABC.
Water pipe runs through point A to C. (a) Construct locus of all points that are:
(i) Equidistant from B and C,

(ii) Equidistant from AB and BC.

(b) A tap T is mounted such that it is:
• Equidistant from AB and BC
• Equidistant from B and C
Label the point where the tap is mounted T.

The diagram shows a triangle ABC. (a) Measure angle ACB.

(b) The point D is above AC, such that AD is 5 cm and CD is 4 cm. By construction, complete the triangle ADC.

(c) The region R lies within the quadrilateral ABCD.
The points in R are:
• nearer to C than A and
• more than 4 cm from B.
By accurate construction, shade the region R.

The diagram shows a triangle ABC. (a) Measure and write the length of BC.

(b) (i) By construction, show all the points inside triangle ABC, that are:
(a) 1.5 cm from AC,
(b) Equidistant from C and A.
(ii) Shade the region, inside triangle ABC, of points that are:
• more than 1.5 cm from AC
and
• nearer to C than A

The diagram shows a quadrilateral ABCD. (a) Explain why A, B, C and D lie on a circle.

(b) Find, by construction, the point O, equidistant from all the vertices.

(c) Find, by accurate construction, the region, inside the quadrilateral, containing the points, P such that:
• P lies nearer to CD than DA,
• P lies nearer to CD than CB.
Shade this region.

(d) Describe the locus of a point Q, which is equidistant from AB and BC, if Q lies:
(i) On the plane ABCD,

(ii) In space.

The diagram shows a map of four villages A, B, C and D. (i) Using a scale of 1 cm to represent 2.5 km, make an accurate drawing of the map on the space provided.
CD has been drawn for you.

(ii) Measure and write down the size of the angle ABC.

(iii) Find the actual distance from village B to C.

(iv) Describe the locus of all points that are equidistant from C and D.

(v) Another village E is located on the map such that it is:
(a) 7.5 km away from village B,
(b) equidistant from BC and CD,
(c) closer to A than C.
On your scale drawing, by construction, mark the location of the village E.

The diagram represents a triangular field ABC.
Scale: 1 cm to 50 m. (a) Find the actual distance AB.

(b) Construct the locus of all points, inside the field, that are:
(i) 150 m from AB,
(ii) Equidistant from AB and BC.
(c) A tree is to be planted inside the field so that it is:
• Less than 150 m from AB, and
• Closer to BC than to AB.
Shade the possible region in which the tree can be planted.