Line segment AB = 40 touches a circle of radius 75 with center O at point B. The circle intersects line segment AO at point D. Find AD.
Since OB is the radius, and point B is longing for touching the segment AB of the circle, then AB is perpendicular to OB, and therefore the triangle AOB is rectangular.
From the right-angled triangle AOB, by the Pythagorean theorem, we determine the length of the hypotenuse OA.
OA ^ 2 = OB ^ 2 + AB ^ 2 = 75 ^ 2 + 40 ^ 2 = 5625 + 1600 = 7225.
ОА = 85 cm.
The segment OD is the radius of the circle, OD = R = 75 cm, then AD = OA – OD = 85 – 75 = 10 cm.
Answer: The length of the segment AD is 10 cm.
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