Algebra 2 need help

Question

A circle has a radius of 4 and is centered at the origin. The line y=2 intersects the circle to form a chord. What is the length of the chord. Round your answer to two decimals.

Answer 1

1- Draw the y and x -axis.

2-Draw a circle with radius equal 4 and its center at the origin.

3- At y= 2 units draw a horizontal line. This line will intersect the circle at points A and B , and intersect y -axis at point C. The length of the chord is AB and AB= 2 CA

4- Draw a line between the origin O and point A. Now you will have a right triangle OCA.

The length of OA = 4 units because OA is the radius of the circle.

The length of OC = 2 units .

5- Use the Pythagorean theorem

OA² = OC² + CA²

CA² = OA² - OC²

= 4² - 2²

= 16 - 4 = 12

CA = √12

AB = 2 CA = 2 √12 = 6.93

Answer 2