Mathematics
Construct a ΔABC with BC = 6.5 cm, AB = 5.5 cm and AC = 5 cm. Construct the incircle of the triangle. Measure the radius of the incircle.
Answer
Steps of construction :
Draw a line segment BC = 6.5 cm.
Cut an arc from C of 5 cm and an arc of 5.5 cm from B.
Mark the point as A where the arcs from B and C intersect.
Join A, B and C. Hence, the △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 incircle is 1.5 cm.
Related Questions
Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.
Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon.
(i) Construct a ΔABC in which BC = 5 cm, AB = 6.5 cm and ∠ABC = 120°.
(ii) Construct a circle circumscribing ΔABC.
(iii) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
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.