In an equilateral triangle of side?24cm, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle [Take?root3?=1.732]
ΔABC is an equilateral triangle.
AB = BC = CA = 24 cm.
O is the incentre of the equilateral ΔABC.
In ΔBOD and ΔCOD,
∠OBD = ∠OCD (30°)
∠ODB = ∠ODC (Radius is perpendicular to the tangent at the point of contact)
OD = OD (Common)
∴ ΔBOD ΔCOD (AAS Congruence criterion)
⇒ BD = CD (CPCT)
In ΔBOD
Radius of the circle, OD =
Area of the remaining portion
= Area of equilateral ΔABC – Area of the incircle