Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the m

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What’s inside this PDF?

Question: Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the measure of the angle ∠AOB, where O is the center of the circle?

Options:

30°
60°
120°
90°

Correct Answer: 120°

Solution:

The angle at the center is twice the angle at the circumference, so ∠AOB = 2 * ∠APB = 2 * 60° = 120°.

Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the m

Practice Questions

Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the measure of the angle ∠AOB, where O is the center of the circle?

30°
60°
120°
90°

Questions & Step-by-Step Solutions

Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the measure of the angle ∠AOB, where O is the center of the circle?

Step 1: Identify the points involved in the problem. We have two circles that intersect at points A and B.
Step 2: Recognize that point P is a point on one of the circles, and we are given the angle ∠APB, which is 60°.
Step 3: Understand the relationship between the angle at the center of the circle (∠AOB) and the angle at the circumference (∠APB).
Step 4: Recall the rule that states the angle at the center (∠AOB) is twice the angle at the circumference (∠APB).
Step 5: Apply this rule: ∠AOB = 2 * ∠APB.
Step 6: Substitute the value of ∠APB into the equation: ∠AOB = 2 * 60°.
Step 7: Calculate the result: ∠AOB = 120°.

Angles in Circles – The relationship between angles at the center and angles at the circumference of a circle.

Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the m

What’s inside this PDF?

Two circles intersect at points A and B. If the angle ∠APB is 60°, what is the m

Practice Questions

Questions & Step-by-Step Solutions

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