Mathematics
Using ruler and compasses only, draw an equilateral triangle of side 5 cm and draw its inscribed circle. Measure the radius of the circle.
Answer
Steps of construction :
Draw a line segment BC = 5 cm.
From B and C cut an arc of 5 cm.
Mark the point as A which is intersection of the two arcs.
Join A, B and C. Hence, the equilateral △ABC is formed.
Draw the (internal) bisectors of ∠B and ∠C. Let these bisectors meet at point I.
From I, draw IN perpendicular to the side BC.
With I as centre and radius equal to IN, draw a circle. The circle so drawn touches all the sides of the △ABC, and is the required incircle of △ABC.
On measuring IN, we get the radius of the incircle.
Hence, the radius of the incircle = 2.3 cm.
Related Questions
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.
Construct a triangle with sides 3 cm, 4 cm and 5 cm. Draw its circumcircle and measure its radius.
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 △ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.