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SSAT Upper Level
Quantitative (Math)

Length of Chord in a Circle

Hard Geometry And Measurement Circles

Consider a circle with a diameter of 14 cm. A chord in this circle is drawn, and the distance from the center of the circle to the chord is 4 cm.

What is the length of the chord?

To solve for the length of the chord, you can use the following relationships:

If a chord is at a distance $d$ from the center of the circle and the radius is $r$, the length of the chord $L$ can be calculated using the formula:

$$L = 2 imes ext{sqrt}(r^2 - d^2)$$

Hint

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