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GRE
GRE Quantitative Reasoning Section

Distance from Center to Chord in Circle

Very Hard Geometry Circles

In a circle with a radius of $r$, a chord of length $c$ is drawn. The distance from the center of the circle to the chord is denoted as $d$. Given that the relationship between the radius, chord, and distance from the center is expressed by the formula:

$$d = rac{1}{2} ext{c} imes rac{ ext{r}}{ ext{sqrt}( ext{r}^2 - rac{c^2}{4})}$$

Assume the following values: the radius $r$ is 10 units and the chord length $c$ is 16 units. Determine if the distance $d$ is greater than, less than, or equal to 5 units.

Hint

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