Mathematics
Using a ruler and a pair of compasses only, construct :
(i) a triangle ABC, given AB = 4 cm, BC = 6 cm and ∠ABC = 90°.
(ii) a circle which passes through the points A, B and C and mark its centre as O.
Constructions
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Answer
(i) Steps of construction :
Draw a line segment BC = 6 cm.
Draw the perpendicular from point B and cut AB from that perpendicular such that AB = 4 cm.
Join points A, B and C.
Hence, the △ABC is formed.
(ii) Steps of construction :
In the above triangle, draw the perpendicular bisector of AB and BC. Let these bisectors meet at the point O.
With O as center and radius equal to OA, draw a circle. The circle so drawn passes through the points A, B and C, and is required circumcircle of △ABC.
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Using ruler and compasses only :
(i) Construct a triangle ABC with the following data :
Base AB = 6 cm, AC = 5.2 cm and ∠CAB = 60°.
(ii) In the same diagram, draw a circle which passes through the points A, B and C, and mark its centre O.