SOLUTION: The radius of a circle is 5 cm and a chord of it is at a distance of 4 cm from the center. What is the length of the chord in cm?
Algebra ->
Circles
-> SOLUTION: The radius of a circle is 5 cm and a chord of it is at a distance of 4 cm from the center. What is the length of the chord in cm?
Log On
You can put this solution on YOUR website! If you draw out the picture, or use the picture given by the book, then you'd see that a right triangle forms with legs of 'x' and 4. The hypotenuse is 5.
So
a = x
b = 4
c = 5
Let's use the pythagorean theorem to find x
a^2 + b^2 = c^2
x^2 + 4^2 = 5^2 ... plug in the given info; isolate x
x^2 + 16 = 25 ... square each value
x^2 + 16-16 = 25-16 ... subtract 16 from both sides
x^2 + 0 = 9
x^2 = 9
sqrt( x^2 ) = sqrt( 9 ) ... Apply the square root to both sides
x = 3
The leg of 3 represents exactly half of this chord.
(