An equilateral triangle is circumscribed about a circle of radius 17.32 cm. What is the perimeter of the triangle?
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Answer:
In the above image equilateral triangle ABC is circumscribed about a circle with radius
=
10
√
3
units. Notice that the sides of the triangle are tangent to the circle, we draw a line segment from the center O to the vertex A, we also draw the radius OD. OA bisects angle A to two 30 degrees parts. And OD is perpendicular to AC.
Triangle OAD is 30-60-90 triangle, the sides have a ratio of:
1
:
√
3
:
2
, hence: AD
=
10
√
3
⋅
√
3
=
30
units. Since OD bisects AC, we conclude that each side of the triangle ABC is 60 units therefore the perimeter is
3
⋅
60
=
180
units.
Step-by-step explanation:
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