An equilateral triangle is inscribed within a circle with radius = 4.
What is the perimeter of the triangle?
What is the perimeter of the triangle?
in an equilateral triangle, the centroid, orthocentre, circumcentre etc all coincide.
well known property is that centroid divides the median in the ratio 2:1
if i connect the center of the circle O to the three vertices of the triangle say OA, OB, OC- then,
OA= OB=OC = 2/3 of the median (according to the centroid division ratio)
OA, OB and OC are infact the radius of the circle = 4
therefore say OA = 2/3 of median = 4.
median= 6.
In equilateral triangle median is the height of the triangle.
height of equilateral triangle is root (3)/2 * side of the triangle= 6
therefore side of the triangle is 6*2 / root(3)
perimeter = 3 * (12/ root (3) ) => 12 root(3)
Hope this helps!
