Çözüldü Trigonometry - The Pythagorean Theorem (8th Grade)

For an ABCD inscribed rectangle in a circle, ∡CDB = π / 6 radians, |AD| = 5 cm, and a point E on the circle |AE| = 6 cm, what is the length of |CE| ?

A) 6
B) 8
C) 6√2
D) 9
E) 10

|BD| = |AC| = Diameter of the circle
The angle ∡AEC that subtends [AC], which is another diameter, must be 90°, so [AE] ⊥ [CE] and then ΔAEC is a right triangle.
Applying the Pythagorean Theorem on ΔAEC, |CE| = { [ 5 / sin(π / 6) ]^2 - 6^2 }^0.5 = (10^2 - 36)^0.5 = √64 = 8 cm.

Source (Turkish): "Türkiye Geneli TYT Deneme Sınavı - 5", Sınav Kodu: 1205, A Kitapçığı, Özdebir Yayınları, Sayfa 23, Soru 30, Yanıtlar yok