The diagram shows an accurate drawing of triangle ABC.

(a)
By constructing appropriate lines on the diagram, mark the point P on AB such that P is equidistant from AC and BC.
(b)
Write down the bearing of P from A.

Answer ... °

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Worked solution

1. Construct the angle bisector of the angle formed by $AC$ and $BC$.

Using compasses and ruler, construct the angle bisector of $\angle ACB$ . This is the locus of points equidistant from the two lines $AC$ and $BC$ .

2. Mark the required point on $AB$.

Let the constructed angle bisector of $\angle ACB$ meet $AB$ at $P$ . Mark this intersection point as $P$ .

Answer

$P$ is the point where the angle bisector of $\angle ACB$ meets $AB$ .

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