An eqilateral triangle is inscribed in a circle of length 6cm .Find the radius of the circle
Dear student,
Consider the below figure where ABC is an equilateral triangle, let AM be a median and O is the point of intersection of the three medians of the triangle and also the centre of the inscribing circle.
In triangle B A M, angle B A M = a = (1/2)(60) = 30 degrees.
In triangle B O M, angle B O M = 2 a = 60 degrees
B M = 1/2 BC = (1/2)(6) = 3 units
radius r = OB = 3/(sin 60) = 2√3 units.
Consider the below figure where ABC is an equilateral triangle, let AM be a median and O is the point of intersection of the three medians of the triangle and also the centre of the inscribing circle.
In triangle B A M, angle B A M = a = (1/2)(60) = 30 degrees.
In triangle B O M, angle B O M = 2 a = 60 degrees
B M = 1/2 BC = (1/2)(6) = 3 units
radius r = OB = 3/(sin 60) = 2√3 units.