Question

Use ruler and compasses only for this question. Draw a circle of radius $$4$$ cm and mark two chords $$AB$$ and $$AC$$ of the circle of length $$6$$ cm and $$5$$ cm respectively.
Construct the locus of points, inside the circle, that are equidistant from $$AB$$ and $$AC$$.

Answer 1

Mark a point $$A$$ on this circle
Taking $$A$$ and centre and $$6$$ cm radius construct an arc which cuts the circle at $$B$$.
Again with $$5$$ cm radius, construct another arc which cuts the circle at $$C$$.
Construct the perpendicular bisector of $$AC$$.
Here any point on it will be equidistant from $$A$$ and $$C$$.
Construct the angle bisector of$$\angle A$$ which intersects the perpendicular bisector of $$AC$$ at the point $$P$$.
Hence, $$P$$ is the required locus