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The diagram shows triangle ABC - OCR - GCSE Maths - Question 7 - 2018 - Paper 4
Question 7
The diagram shows triangle ABC. (a) Construct the bisector of angle BAC. (b) Construct the perpendicular bisector of AC. (c) Shade the region inside triangle ABC ... show full transcript
Worked Solution & Example Answer:The diagram shows triangle ABC - OCR - GCSE Maths - Question 7 - 2018 - Paper 4
Step 1
Construct the bisector of angle BAC.
Answer
To construct the bisector of angle BAC, follow these steps:
- Place the compass point on vertex A, and draw an arc that intersects sides AB and AC. Label the intersection points as D and E.
- Without changing the compass width, place the compass point on D and draw an arc, and then on E, draw another arc such that both arcs cross. Label the intersection of these arcs as F.
- Draw a straight line from point A through point F. This line is the angle bisector of BAC.
Step 2
Construct the perpendicular bisector of AC.
Answer
To construct the perpendicular bisector of segment AC, proceed as follows:
- Open your compass to more than half the length of segment AC. With the compass point on point A, draw an arc above and below the segment AC.
- Without altering the compass width, repeat this step with the compass point on point C, creating two arcs that intersect the first arcs in two points. Label these points as G and H.
- Draw a straight line through points G and H. This line is the perpendicular bisector of AC.
Step 3
Shade the region inside triangle ABC that is nearer to AC than to AB and nearer to A than to C.
Answer
To shade the correct region:
- Identify the area of triangle ABC that is closest to line AC. This area will be defined by the angle bisector you previously constructed, indicating proximity to AC.
- Next, delineate the area that is closer to point A than to point C. This can be visualized by drawing a line segment from A to the midpoint of BC.
- The final shaded region will be the area within triangle ABC that satisfies both conditions: it is nearer to line AC than to line AB and also nearer to point A than to point C.