Question

In the diagram, point O is the center of the circle and AC and BD intersect at point E. If m∠AOB = 90° and m∠COD = 16°, what is m∠CED?
A. 37°
B. 48°
C. 53°
D. 62°

Answer 1

answer is 37 or 48.

Answer 2

Answer: C. 53°

Step-by-step explanation:

Here,  Point O is the center of the circle, AC and BD are the chord of the circle, E is the intersection point of AC and BD,

m∠AOB = 90° and m∠COD = 16°

To find : m∠CED

When we join points B and C (By construction)

Then by the center angle theorem,

We get, m∠AOB = 90° ⇒ m∠ACB = 45°

Similarly, by joining points A and D,

m∠AOB = 90° ⇒ m∠ADB = 45°

Since, triangles COD and CBD are made by the same arc CD inside the circle having the center O.

Thus, m∠CBD = m∠COD/2 = 16/2 = 8°

⇒ m∠CBD =  8°

Now, m∠CED = m∠CBD + m∠ACB  (Exterior angle)

⇒  m∠CED = 8° + 45° = 53°

Therefore, the measurement of the angle CED = 53°

⇒ Option C is correct.