Q1. If the angle at the circumference is 30 degrees, what is the angle at the center?
✔ The angle at the center is double the angle at the circumference. Therefore, 30 multiplied by 2 equals 60.
Q2. What is the reflex angle if the minor central angle is 100 degrees?
✔ The reflex angle is found by subtracting the minor angle from 360. So, 360 minus 100 equals 260.
Q3. Which theorem states that the central angle is twice the inscribed angle?
✔ The Angle at Center Theorem specifically defines the relationship between central and inscribed angles on the same arc.
Show transcript
[Slide 1] Understanding Circle Angles
Welcome back. Today we solve numerical problems using circle theorems. Remember, angles at the center are twice those at the circumference. This helps us find missing values quickly.
[Slide 2] Angle at Center Theorem
The main rule is the angle at the center theorem. It states the central angle is twice any inscribed angle. We use this relationship to set up equations.
[Slide 3] Solving a Numerical Problem
Let's try an example. If angle ABC is forty degrees, what is angle AOC? Simply multiply forty by two to get eighty degrees. This gives the minor central angle.
[Slide 4] Avoiding Calculation Errors
A common mistake is ignoring the reflex angle. Sometimes questions ask for the larger angle around the center. Always check if you need three hundred sixty minus your answer.
[Slide 5] Key Takeaways Summary
To recap, identify the shared arc first. Apply the doubling rule for central angles. Finally, check if a reflex angle is required. Practice these steps for board exams.