ConstructionModerate1 mark
10(c)
Use ruler and compass for this question. Construct a circle of radius 4.5 cm. Draw a chord AB = 6 cm.
Find the locus of points equidistant from A and B. Mark the point where it meets the circle as D.
Topic: Loci
Previous-year question practice database
Answer
Solution diagram
Exam answer
The locus of points equidistant from A and B is the perpendicular bisector of AB.
Construction: Draw the perpendicular bisector of chord AB and extend it to meet the circle at D.
Answer:
D is the point where the perpendicular bisector of AB meets the circle.
Explanation
Every point on the perpendicular bisector of a segment is equidistant from its two endpoints. Therefore the required locus for points equidistant from A and B is the perpendicular bisector of AB.
More from Loci (Locus and Its Constructions)
construct the locus of points which are equidistant from AB and BC. Mark the point where the circumcircle and locus meet, as D.2026Construct the locus of points equidistant from B and C.2024Construct the locus of points equidistant from A and B.2024Mark the point which satisfies both the conditions (a) and (b) as O. Construct the locus of points keeping a fixed distance OA from the fixed point O.2024Construct the locus of points which are equidistant from BA and BC.2024Join AD and find the locus of points which are equidistant from AD and AB. Mark the point where it meets the circle as C.2020