Because ∠ABC and ∠CED correspond to the same radian, ∠ABC=∠CED, so △ABC and △ADE are similar triangles, that is, their area ratio is equal to the square of the ratio of their three sides. That is | de |/| BC | = | AB |/| AE | = | AC |/| AD | = SQRT (3/4).

Because BC is the diameter of a circle, ∠BEC=90 degrees, ∠ Abbe =60 degrees, ∠BAC=30 degrees.

The arcuate area is equal to the sector area minus the area of the extra triangle, ∠DOE=2∠ABE= 120 degrees, so the sector area s 1 = π r2x (120/360) = (2/3) π r, and △DOE is.