The chord of the circle, equal to a, contracts the arc by 90 degrees. Find the radius of the circle.
| September 23, 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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