Réponse :
Explications étape par étape :
Given that OE bisects AB, we can conclude that AE = EB (since AO is equal to BO in a circle).
From the given information, we have AD = 12 cm and ED = 8 cm.
Since OE bisects AB, we can write AE + EB = AB. Therefore, AE = EB = 1/2 * AB = 1/2 * 12 = 6 cm.
Now, since OD is perpendicular to AE, we can use Pythagoras theorem to find the value of x (OD).
Thus, x^2 = AE^2 + OD^2
x^2 = 6^2 + 8^2
x^2 = 36 + 64
x^2 = 100
x = 10 cm
Now, we can determine the radius OB in terms of x using the Pythagoras theorem.
OB^2 = OE^2 + x^2
OB^2 = 12^2 + 10^2
OB^2 = 144 + 100
OB^2 = 244
OB = √244
OB = 2√61 cm
Therefore, the length of the radius OB is 2√61 cm.
