An equilateral triangle with sides of length 6 is inscribed in a circle

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 331 People

An equilateral triangle with sides of length 6 is inscribed in a circle. What is the diameter of the Circle?
A:5.2
B:6
C:6.9
D:7.5

Answered by maham237 @ 22/12/2020

Answer:

The diameter is 6.92 unit.

Step-by-step explanation:

Given : An equilateral triangle with sides of length 6 is inscribed in a circle.

To find : What is the diameter of the Circle?

Solution :

First we picture the situation.

Refer the attached figure below.

We that the angles of equilateral triangle is 60 degrees.

Then, we divide the triangle into two parts to solve the radius.

As,

∠ACD is 60°

$\angle OCD=\frac{\angle ACD}{2}$

$\angle OCD=\frac{60}{2}=30^\circ$

In triangle OCD,

$\cos 30^\circ= \frac{CD}{OC}$

$\frac{\sqrt{3}}{2}=\frac{3}{r}$

$r=\frac{3\times 2}{\sqrt{3}}$

$r=2\sqrt{3}$

$r=3.4641$

Diameter = 2r=2(3.4641)=6.92 unit.

Therefore, The diameter is 6.92 unit.

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