Given equilateral ΔPQR with its sides 4.6 cm each.
To construction : In circle of this triangle.
Steps of construction :
(1) Draw a line segment PQ = 4.6 cm
(2) Taking P as center and with 4.6 cm as radius draw an arc.
(3) Taking Q as center and with 4.6 cm as radius draw another arc, which intersect each other at R.
(4) Join PQ and QR, PQR is the required equilateral triangle.
(5) Now draw the bisectors of ∠RPQ and ∠RQP, which intersect each other at O.
(6)d Draw MT ⊥ PQ from O.
(7) Taking O as centre and radius equal to OM draw a circle which touches the three sides of ΔPQR.
This is required incircie of ΔPQR.
∵ The internal angles ans sides of an equilateral triangle are equal so its circumcentre and in centre are concurrent.
