Hi All,

I have posted a video on YouTube to discuss about Equilateral Triangle Inscribed in A Circle



And, Length of Major and Minor Arc formed by a Side of an Equilateral Triangle Inscribed in a Circle



Following is Covered in the Video

¤ Equilateral Triangle Inscribed in a Circle : Properties
-> Measure of Center Angle
-> Height of Triangle
-> Base of Triangle
-> Area of Triangle

¤ Length of Minor Arc formed by one side of the triangle
¤ Length of Major Arc formed by one side of the triangle

Measure of Center Angle



Measure of Center Angle ∠AOB = ∠AOC = ∠BOC = 120° ( Watch this video to understand how )
Hint: ∠ACB = 60°, so center angle will be twice of it
Also, ∠OAB = ∠OBA = 30°
∠OBC = ∠OCB = 30°
∠OAC = ∠OCA = 30°

Height of Triangle

Height of triangle, h (AD) = \(\frac{3r}{2}\)
( Watch this video to understand how )

Base of Triangle

Base of triangle, BC = √𝟑 r ( Watch this video to understand how )

Area of Triangle

Area of triangle ABC = \(\frac{3√𝟑 r^2}{4}\)
( Watch this video to understand how )

Length of Minor Arc formed by one side of the triangle



Length of Minor Arc AB = \(\frac{120˚}{360˚}* 2 \pi \) r = \(\frac{2\pi r}{3}\) (as Minor angle ∠AOB = 120˚)
( Watch this video to understand how )

Length of Major Arc formed by one side of the triangle

Length of Major Arc AB = \(\frac{240˚}{360˚} * 2\pi r\) = \(\frac{4\pi r}{3}\) (as Major angle ∠AOB = 240˚)
( Watch this video to understand how )

Hope it helps!