Question

Q16. O is the centre of the circle,
and chord AC is equal to its
radius, What is the measure of
ZAOC?​

Answer 1

Answer:

∠BCD = ∠ABC (alternate ∠s in AB//CD) . . . so ∠BCD = 35°

∠OCB = ∠OBC (base ∠s of isosceles ∆OCB) . . . so ∠OCB = 35°

∠OCD = ∠OBC + ∠BCD = 35° + 35° . . . so ∠OCD= 70°

∠ODC = ∠OCD (base ∠s of isosceles ∆OCD) . . . so ∠ODC = 70°

∠COD = 180° - ∠OCD - ∠ODC (sum of interior ∠s of ∆OCD) = 180° - 70° - 70° = 40° . . . so ∠COD = 40°

Finally, ∠CED = ∠COD2 (∠ at circumference = half ∠ at centre)

So ∠CED = 40°2=20°