Mathematics
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.
Answer
(i) Steps of construction :
Draw a line segment AB = 6 cm.
Cut an arc of 5.2 cm from A.
Draw a line segment from B such that angle between the line and AB = 60°.
Mark the point as C where the arc from A and line segment from B meets.
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.
Related Questions
Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.
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.
Construct a triangle ABC with BC = 6.4 cm, CA = 5.8 cm and ∠ABC = 60°. Draw its incircle. Measure and record the radius of incircle.
Construct a triangle with sides 3 cm, 4 cm and 5 cm. Draw its circumcircle and measure its radius.