Question

An equilateral triangle of side 11cm inscribed in a circle. Find radius of the circle.

Answer 1

well it's a example to how to slove the question like that...



Refer the figure above. The following concepts are important before we solve:

i) Since the triangle is Equilateral (side S = 6 cm), it’s Perpendicular Bisector (Altitude) = Median = Angle Bisectors. And all meet at the same point (O).

ii) In order to inscribe a triangle within a circle, the Centre of the Circle should be the Circum-centre (that is where the perpendicular bisectors meet). Thus, here O being the meeting point of the perpendicular bisectors, the centre of the circle.

iii) For the circle, radius is denoted by “a”

iv) Medians gets intersected in the ratio 2:1 at the point of intersection. Thus, longer segment is 2/3 of the median length and shorter segment in 1/3 of the median length

v) We know that for an equilateral triangle, Height (perpendicular) = (√3/2).(side)

Here, Height = (√3/2).S

From (iv), we now get that length of the line segment denoted by “a” = (2/3). Height =

T(2/3).(√3/2).S =(S/ √3) = Radius

So, Radius = (6/ √3) = 2√3 cm

hope it will help uh