Question

If a chord is 10 inches from the center of the circle. The circle has a radius of
26 inches. Find the length of the chord .

Answer 1

the length of the chord is 48 inches

Explanation

Step 1

Diagram

Let C represents the length of the chord

so, we can solve the rigth triangle to find the C length

Step 2

Let C represents the length of the chord

solve for C in the rigth triangle,

to do that, we can use the Pythagorean theorem, is states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle),so

$\begin{gathered} 10^2+(\frac{C}{2})^2=26^2 \\ 100+\frac{C^2}{4}=676 \\ subtract\text{ 100 in both sides} \\ 100+\frac{C^{2}}{4}-100=676-100 \\ \frac{C^2}{4}=576 \\ multiply\text{ both sides by 4} \\ \frac{C^{2}}{4}*4=576*4 \\ C^2=2304 \\ square\text{ root in both sides} \\ \sqrt{C^2}=\sqrt{2,304} \\ C=48 \end{gathered}$

so,

the length of the chord is 48 inches

I hope this helps you