How to find the length of a chord

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ACT Math › How to find the length of a chord

Questions 1 - 3

1

A circle has a maximum chord length of inches. What is its radius in inches?

Explanation

Keep in mind that the largest possible chord of a circle is its diameter.

This means that the diameter of the circle is inches, which means an -inch radius.

Remember that ,

$\16=2r\ \ \frac{16}{2}=\frac{2r}{2}\ \ 8=r$

2

In the figure below, and are radii of the circle. If the radius of the circle is 8 units, how long, in units, is chord ?

Circle

$8\sqrt2$

$16\sqrt2$

$4\sqrt2$

Explanation

The radii and the chord form right triangle . Use the Pythagorean Theorem to find the length of .

$8^2+8^2={AB}^2$

3

In the circle with center A, shown below, the length of radius $\overline{AB}$ is 4 mm. What is the length of chord $\overline{BC}$ ?

Circle_chord

$2\sqrt{2}$

$2\sqrt{3}$

$4\sqrt{2}$

$4\sqrt{3}$

$8\sqrt{2}$

Explanation

In order to solve this question, we need to notice that the radii of the circle and chord $\overline{BC}$ form a right triangle with $\overline{BC}$ as the hypotenuse. We can use the Pythagorean theorem to find chord $\overline{BC}$ .

$4^2 + 4^2 = \overline{BC}^2$

$32 = \overline{BC}^2$

$\sqrt{32} = \overline{BC}$

$\sqrt{16\cdot 2} = \overline{BC}$

$4\sqrt{2} = \overline{BC}$

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