Question

Q 45 What is the difference in the areas of incircle and circumcircle of an equilateral triangle of side 6cm
2
Ops: A. 18.36 cm
B.O 28.26 cm
2
2
C.
0 12.28 cm
2
D.
36.42 cm
reset answer​

Answer 1

Answer:

Step-by-step explanation:

  Draw a line segment BC=6cm

⇒   Take B and C as a center with radius 6cm and draw an arc meeting at point A.

⇒   Join AB and AC. We get ABC as the  required equilateral triangle.

⇒   Draw a perpendicular bisector on sides AB,BC,AC meeting at point O.

⇒   Take O as the center with radius equal to OA and draw a circle.

⇒   We have to measure radius of the circumcircle, i.e the measure of length of OA.

ALTERNATE

Let a be the side of the equilateral triangle ABC.

∴ AB=BC=AC=a

and since ΔABC is an equilateral triangle

∠A=∠B=∠C=60  

Given, radius of the circumcircle, r=6cm

Since the triangle ABC is equilateral, its perpendicular bisector i.e. the median meet at the same point O which is the centre of the in circle

∴ AD is the perpendicular bisector of BC.

⇒ BD=DC= 1/2

​and OB is the angle bisector of ∠B.

∴∠ABO =∠ OBD =  60  /2

                             =30  

In rt Δ ODB sin 30  =OD/OB

OD ⇒OD=  OD/r

⇒OD=3cm

∴ Radius of the incircle =3cm.