Math Problem Statement
The size of ∠OBC is
Solution
To determine the size of , we can use the following approach:
- Since is the center of the circle, , , and are radii of the circle.
- We are given that , which is the angle at the center.
Now, let's apply the angle subtended by the same arc theorem, which states that the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at the circumference.
- Arc subtends at the center, which is .
- Therefore, the angle subtended by arc at point on the circumference, , will be half of .
Thus, is 60°.
Let me know if you need more details or have further questions!
Here are 5 related questions for deeper understanding:
- What is the measure of in this circle?
- How can you prove that is isosceles?
- What is the total sum of the interior angles in ?
- How would you calculate the length of if the radius of the circle is known?
- How does the property of cyclic quadrilaterals apply to this diagram?
Tip: Always remember that angles at the center of a circle are twice the angles on the circumference subtended by the same arc.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circles
Angles at the center and circumference
Formulas
Angle at center = 2 × Angle at circumference
Theorems
Angle subtended by the same arc theorem
Suitable Grade Level
Grades 9-11
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