Question

There is a circle with an 8-foot chord. The midpoint of the chord is located 3 feet from the center of the circle. What is the length of the diameter of the circle?

Answer 1

did you try drawing this? If you draw divide a line segment of length 8 in half, what do you get?

Answer 2

so a midpoint divides that 8 into two 4's
the length from the center is 3
so if you draw a line segment from the center to where the chord ends at on the circle then you would have a right triangle
what theorem is famous for finding another side given 2 two sides of a right triangle

Answer 3

The line from the chord midpoint to the center of the circle is perpendicular to the chord. This line also bisects the chord (cuts it in half). So the half chord (4ft) and line from the chord midpoint to the circle center(3ft) form a right angle. They also form two sides of a right triangle. The third side, the hypotenuse, is the radius of the circle. Find the radius by the Pythagorean Theorem. radius = sqrt(4^2+3^2). The radius is 5. The diameter is twice the radius, 10.

Answer 4

very good simbasocks