Geometry Problem 1362: Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps.

Proposition

The figure below shows an equilateral triangle ABC inscribed in a circle O. Circle Q is tangent to AB, AC, and arc BC at E, F, and D, respectively. S is the area of the blue lunula and S1 is the area of the yellow circle. Prove that S / S1 = 5 / 4.
 


Geometry Problem 1362: Equilateral Triangle Inscribed in a Circle, Lunula, Ratio of Areas, Tangent, Sketch, iPad Apps

See solution below


Sketch and Typography of problem 1362 using iPad Apps


Sketch and typography of Geometry Problem 1362 using iPad Apps, Tutor

See solution below


 


Geometry Problem 1362 Solution(s)