The chord of the circle, equal to a, contracts the arc by 90 degrees. Find the radius of the circle.

Let’s construct the radii ОА and ОВ.

The arc AB, by condition, is equal to 90, then the central angle AOB = 90, since it rests on this arc. Then triangle AOB is rectangular and isosceles, OA = OB = R.

Then AB ^ 2 = 2 * R ^ 2.

R = AB / √2 = a * √2 / 2 cm.

Answer: The radius of the circle is a * √2 / 2 cm.

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