Equilateral triangle and circle
Q01. Diagram
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Q02. Equilateral triangle and circle
Construction
- Draw an equilateral triangle
- Draw 1st circle inscribed triangle
- draw 2nd circle tangent circle and two sides
- draw 3rd circle tangent 2nd circle and two sides
- Find the area of the 3rd circle
Find area of smallest circle
- Let each side be 1
- Height of triangle h = Sqr(1 + (1/2)^2) = Sqr(3)/2
- Radius of 1st circle r1 = h/3 = Sqr(3)/4
- Radius of 2nd circle r2 = (r1)/3 = Sqr(3)/(3*4)
- Radius of 3rd circle r3 = (r2)/3 = Sqr(3)/(3*3*4) = Sqr(3)/36
- Hence area of 3rd triangle = pi*(r3)^2 = 3*pi/(36^2) = 0.0023148
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Q03. Questions
Questions
- 1. Find area of 4th circle which tangent 3rd circle and two sides
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