Find a chord subtending a 90 ° arc if the radius of the circle is 5 cm.

By condition, the chord AB contracts the arc AB = 90. Let us construct from the point O, the center of the circle, the radii OA and OB, to the edges of the chord.

The inscribed angle AOB rests on the arc AB, the degree measure of which is 90, then the central angle AOB = 900, and the triangle AOB is rectangular and isosceles, OA = OB = R = 5 cm.

Then AB ^ 2 = 2 * OB ^ 2 = 2 * 25.

AB = 5 * √2 cm.

Answer: The chord length is 5 * √2 cm.