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The circle above has center O and area 9*pi.  Triangle ABC is equilateral.  Find its area.

 

 Jan 2, 2020
 #1
avatar+2551 
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This is what I did:

 

I noticed that segment AO and OD are radii, and since radii are all congruent, center O must also be the midpoint of AD.

 

I calculated OD because it was a radii.

 

Then I multiplied the value of OD by 2 to get AD. We know know the height of triangle ABC.

 

 

Since ABC Is equilateral, that means angles C and B are 60 degrees.

 

We find that triangles ACD and ABD are 30-60-90 triangles.

 

 

Since we know the height of triangle ABC and we know that triangles ACD and ABD are 30-60-90, can you find the area?

 

Hint: try using the properties of a 30-60-90 triangle.

 Jan 2, 2020
 #2
avatar+11043 
+1

The circle above has center O and area 9*pi.  Triangle ABC is equilateral.  Find its area.

laugh

 Jan 2, 2020

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