Mathematics
Construct a triangle with sides 5 cm, 4 cm and 3 cm. Draw its circumcircle and measure its radius.
Answer
Steps of construction :
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 ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.
Using ruler and compasses only, draw an equilateral triangle of height 6 cm and draw its inscribed circle. Measure the radius of the circle.
(ii) Using a ruler and a pair of compasses only, construct:
(a) a triangle ABC, given AB = 4 cm, BC = 6 cm and ∠ABC = 90°.
(b) a circle which passes through the points A, B and C and mark its centre as O.
Using a ruler and a compass construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of:
(i) Points equidistant from AB and AC.
(ii) Points equidistant from BA and BC.
Hence, construct a circle touching the three sides of the triangle internally.