CGPET 2016 Solved Paper

Given equation of the circle is
x2+y2=a2
where, radius =a
Let ABC be the inscribed equilateral triangle and length of its each sides be I.

Area of ∆ABC=

√3

4

I2
Also, OD=√a2−

I2

4

[from∆ODB]
∴ Area‌of∆OBC=

1

2

×I×√a2−

I2

4

Now, Area of ∆ABC=3×Area‌of∆OBC
⇒

√3

4

I2=3×

I

2

√a2−

I2

4

⇒√3I=3√4a2−I2
⇒ 3I2=9(4a2−I2)
⇒ I2=12a2−3I2
⇒ 4I2=12a2
⇒ I2=3a2
⇒ I=√3a