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.
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