Çözüldü Median to Hypotenuse in Right Triangle - Circle Radius - Pythagorean Theorem - Two-Variable Equation

On a circle whose center is O, for the points A, B, and C that are on the circle, and the point D that is on [BO],
[AD] ∩ [CO] = {E}, if [AO] ⊥ [BO], |AE| = |DE|, |Do| = 6 cm, |BD| = 2 cm, find the length of |CE|.

A) 9 / 2
B) 4
C) 7 / 2
D) 3
E) 2


https://i72.servimg.com/u/f72/19/97/10/39/circle18.png

|CE| = x cm
|AE| = |DE| = |EO| = y cm
x + y = 6 + 2 = 8
(2y)^2 = 8^2 + 6^2 ⇒ y^2 = 100 / 4 = 25 ⇒ y = 5 cm
x = 8 - 5 = 3 cm.