Mathematics
Answer
Steps of construction :
Draw a line segment BC = 4 cm.
With centers B and C, draw two arcs of radius 4 cm which intersect each other at A.
Join AB and AC. Hence, equilateral triangle ABC is formed.
Draw the perpendicular bisectors 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 the required circumcircle of △ABC.
Related Questions
Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
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.
Use ruler and compass, construct a triangle ABC where AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Hence, construct a circumcircle circumscribing the triangle ABC. Measure and write down the radius of the circle.