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

Step-by-step 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+((C)/(2))^2=26^2 \\ 100+(C^2)/(4)=676 \\ subtract\text{ 100 in both sides} \\ 100+(C^(2))/(4)-100=676-100 \\ (C^2)/(4)=576 \\ multiply\text{ both sides by 4} \\ (C^(2))/(4)*4=576*4 \\ C^2=2304 \\ square\text{ root in both sides} \\ √(C^2)=√(2,304) \\ C=48 \end{gathered}`

so,

the length of the chord is 48 inches

I hope this helps you