In a circle with a radius of 1.4, determine the distance from the center to the chord if it intercepts an arc of $120^{\circ}$.

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The leg opposite the $30^{\circ}$ angle is half the hypotenuse.

## Solution

Let $M$ be the foot of the perpendicular dropped from the center $O$ to the chord $A B$. Then $O M$ is the leg of the right triangle $O M A$, lying opposite the angle of $30^{\circ}$. Therefore, $O M=1 / 2 O A=0.7$.

## Answer

0.7.