The diameter of a circle is 170 the circle has two chords of length 26 inches what is the distance from each chord to the center of the circle?

Answer 1

There is an easier way to do this. We know the radius is 170/2 or 85 Lets create a right triangle by drawing a radius from the center fo the circle to the point where the chord intersects the circle and a Perpendicular line from the center of the circle to the chord ( this is the side we will have to solve for). This perpendicular line will bisect the chord so this length will be 26/2= 13

DRAW A PICTURE

Now we can us Pythagorean theorm x^2 + (13)^2 = (85)^2

x^2 +169 = 7225

x^2 =7056. Take the square root of both sides

x=84 There you go

Answer 2

Let's calculate the distance from one of the chords to the center of the circle!

The circle radius is 85. The chord length is 26. So the equilateral triangle to the chord has two sides = 85 each. Calculate the origin angle using the law of cosines,

26^2 = 85^2 + 85^2 - 2(85)(85)cos(O) the origin angle turns out to be 17.6 degrees

Now, construct the line that is the length of the distance from the chord to the origin (H) and you make 2 triangles. the height of the triangle is that length. From either triangle, cos(O/2) = H/85 or

H = 84.