A chord equal to alpha subtracts the arc 90 °. Find the radius of the circle.

univerkov | April 28, 2021 | education

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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