Mathematics
Use ruler and compasses only for the following question. All construction lines and arcs must be clearly shown.
(i) Construct a △ABC in which BC = 6.5 cm, ∠ABC = 60° and AB = 5 cm.
(ii) Construct the locus of points at a distance of 3.5 cm from A.
(iii) Construct the locus of points equidistant from AC and BC.
(iv) Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.
Locus
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Answer
(i) Steps of construction :
Draw a line segment BC = 6.5 cm.
With B as center draw an arc BX, at an angle of 60°.
From BX cut off BA = 5 cm.
Join AC. Hence, ABC is the required triangle.
With A as center draw a circle of radius = 3.5 cm.
Draw CZ, the angle bisector of ∠C.
Mark the points as X and Y where CZ intersects circle with center A.
(ii) The locus of points at a distance of 3.5 cm from A is a circle with radius = 3.5 cm and center A.
(iii) The locus of points equidistant from AC and BC is CZ, the angle bisector of ∠C.
(iv) On measuring, XY = 4.8 cm.
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