Question

Area of an equilateral triangle inscribe in the circle x*2 y*2 2gx 2fy c

Answer 1

Given circle is x2+y2+2gx+2fy+c=0x2+y2+2gx+2fy+c=0------(1)

Let O be the centre and ABC be equilateral triangle inscribed in the circle (1)

0=(−g,−f)0=(−g,−f)

OA=OB=OC=g2+f2−c−−−−−−−−−√g2+f2−c

In ΔOBMΔOBM

sin60∘=BMOBsin⁡60∘=BMOB

BM=OBsin60∘=OB×3–√2BM=OBsin⁡60∘=OB×32

BC=2BM=3–√OBBC=2BM=3OB

Area of ΔABC=3–√4ΔABC=34(BC)2(BC)2

⇒3–√4⇒34×3(OB)2×3(OB)2

⇒33–√4(g2+f2−c)sq.units