Question

An equilateral triangle with sides of length 6 is inscribed in a circle. What is the diameter of the circle?.

Answer 1

Answer:quick check answers

1.C

2.B

3.D

4.B

5.C

Explanation:

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Answer 2

To solve for the diameter of the circle, we have to divide the triangle in to parts to solve for the radius. The angles of the triangle is 60 degrees.

∠ACD is 60°
∠OCD is equal to ∠ACD / 2 which is 60/2 or 30 degrees.

In triangle OCD as shown in the picture attached,
cos 30°= CD / OC
√3 / 2 = 3 / r
r = 3 x 2 /√3
= 3.4641 cm

Therefore, the diameter is 6.93 cm.