Intersecting Circles and Distance Calculation Quiz

What is the relationship between the line passing through the centers of two intersecting circles and the line segment connecting their intersection points?

• The line is a diagonal of the line segment.

• The line is tangent to the line segment.

• The line is the perpendicular bisector of the line segment.

• The line is parallel to the line segment.

If Circle A has a radius of 12 units and CE is 8 units, what is the length of AE?

• 7√2 units

• 6√3 units

• 5√4 units

• 4√5 units

Which theorem is used to calculate the length of AE in the triangle formed by connecting A, C, and E?

• The Pythagorean Theorem

• The Triangle Inequality Theorem

• The Law of Sines

• The Law of Cosines

Given that Circle B has a radius of 9 units and CE is 8 units, what is the length of BE?

• √20 units

• √18 units

• √19 units

• √17 units

What is the approximate total distance between the centers of Circle A and Circle B?

• 14 units

• 12 units

• 13 units

• 11 units