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1 month ago

In the diagram, point O is the center of the circle and AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E. If m∠AOB = 90° and

Mathematics

2 answers:

lawyer [12.5K]1 month ago

6 0

Answer:

Step-by-step explanation:

When I entered 53 into PLATO, it appears to be the correct answer.

Zina [12.3K]1 month ago

5 0

Answer: $53^{\circ}$

Step-by-step explanation:

Given: Point O denotes the circle's center, AC and BD are chords of the circle, while E is where AC intersects BD,

m∠AOB = 90° and m∠COD = 16°

We need to find: m∠CED

By connecting points B and C (construction)

m∠AOB = 90° ⇒ m∠ACB = 45° (based on the center angle theorem)

Similarly, joining points A and D leads to

m∠AOB = 90° ⇒ m∠ADB = 45°

Since triangles COD and CBD share the same arc CD within the circle about center O.

Therefore, m∠CBD = m∠COD/2 = 16/2 = 8°

Thus, m∠CBD = 8°

However, m∠CED = m∠CBD + m∠ACB (using the exterior angle property of the triangle)

Thus, m∠CED = 8° + 45° = 53°

Hence, m∠CED = 53°

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