Mathematics
Construct a triangle with sides 3 cm, 4 cm and 5 cm. Draw its circumcircle and measure its radius.
Answer
Draw a line segment BC = 4 cm.
From B cut an arc of 3 cm and from C cut an arc of 5 cm.
Mark the point as A where the arcs meet.
Join the points A, B and C. Hence, the △ABC is formed.
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 the required circumcircle of △ABC.
Measuring OB we get the radius of the circumcircle.
Hence, the radius of the circumcircle = 2.5 cm.
Related Questions
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.
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.
Draw an equilateral triangle of side 4 cm. Draw its circumcircle.
Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.