MN and NK-tangent line segments drawn to a circle centered at point O, angle MNK = 90 degrees

MN and NK-tangent line segments drawn to a circle centered at point O, angle MNK = 90 degrees, ON = 2√2. Find the radius.

By condition, the angle КNМ = 90. Let’s draw the segments OK and ОМ from the center of the circle to the points of tangency of the straight lines NK and NM. OK = OM as the radii of a circle, and form right angles OKN and OMN.

Then the rectangle is OKNM square, since all angles are right and the two sides are equal.

Consider a right-angled triangle ONM and, by the Pythagorean theorem, determine the side of the square.

ON ^ 2 = OM ^ 2 + NM ^ 2 = 2 * OM ^ 2.

(2 * √2) ^ 2 = 2 * OM ^ 2.

ОМ ^ 2 = 4 * 2/2 = 4 cm.

OM = 2 cm.

Answer: The radius of the circle is 2 cm.