Mathematics
Use 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.
Locus
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Answer
Steps of construction:
Draw BC of length 4.2 cm.
Make angle 60° at B.
With B as center and radius 5 cm, cut off AB = 5 cm.
Join AC, ΔABC required triangle.
Draw BD angle bisector of ∠ABC.
Draw EF || BC at 2 cm from BC, intersects BD at O.
Taking O as centre and 2 cm as radius draw required circle.
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Related Questions
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) ABEUsing 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.
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.
The locus of a point which moves in a plane in such a way that its distance from a fixed point is always constant, is known as :
a square
an equilateral triangle
a circle
a parallelogram