suppose the diameter of a circle is 20in. long and a chord is 16in. long. What is the distance from the center of the circle to the chord
Draw a radius from the center to the end of the chord. THe draw a radius from the center perpendicular to the chord. You have a right triangle, one side is radius (given), one side is 1/2 chord, and your distance. Use the pyth theorm to solve.
If the equation of a circle is (x + 4)2 + (y - 6)2 = 25, its radius is
To find the distance from the center of the circle to the chord, you can use the Pythagorean theorem.
First, draw a radius from the center of the circle to one end of the chord. This will create a right triangle.
Now, draw another radius from the center of the circle perpendicular to the chord. This radius bisects the chord and divides it into two equal parts.
You now have a right triangle with the radius (given) as one side, the distance from the center to the chord as another side, and half of the chord as the hypotenuse.
Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, you can set up the following equation:
(radius)^2 + (distance)^2 = (1/2 chord)^2
In this case, the radius is half of the diameter, so it is 20in/2 = 10in. The chord is given as 16in, so half of the chord is 8in.
Now you can plug in the values into the equation:
(10in)^2 + (distance)^2 = (8in)^2
Simplifying:
100in^2 + (distance)^2 = 64in^2
Subtracting 64in^2 from both sides:
100in^2 - 64in^2 = (distance)^2
36in^2 = (distance)^2
Now, take the square root of both sides:
distance = √(36in^2)
distance = 6in
So, the distance from the center of the circle to the chord is 6 inches.