Mathematics
Using ruler and compasses only,
(i) Construct a ΔABC in which BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC. Measure ∠BCP.
Answer
Steps of construction :
Draw a line BC = 6 cm.
At B, draw a ray BX making an angle of 120° with BC. With B as center and radius 3.5 cm, cut off AB = 3.5 cm.
Join AC. ABC is the required triangle.
Draw perpendicular bisector of BC which cuts BC at point O. With O as center and radius = OB, draw a circle.
Draw angle bisector of ∠ABC which meets the circle at point P. Thus, point P is equidistant from AB and BC.
Measure ∠BCP.
On measuring, ∠BCP = 30°.
Related Questions
A and B are fixed points 5 cm apart. The locus of the point P is the set of those points for which AP = 4 cm and the locus of Q is the set of those points for which BQ = 3.5 cm.
Construct the loci of P and Q and the points of intersection of the two loci. How many such points are there?Using only a ruler and compasses, construct ∠ABC = 120°, where AB = BC = 5 cm.
(a) Mark two points D and E which satisfy the condition that they are equidistant from both BA and BC.
(b) In the above figure, join AE and EC. Describe the figures.
(i) ABCD
(ii) BD
(iii) ABEUse a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ABC = 60° and AB = 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ABC of ΔABC.
Using ruler and compasses construct
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of points equidistant from A and C.
(iii) a circle touching AB at A and passing through C.