The straight line touches the circle with center O at point A. On the tangent on opposite sides of point A

The straight line touches the circle with center O at point A. On the tangent on opposite sides of point A, points B and C are marked such that OB = OC. Find AB if AC = 6cm.

The segment OA is a segment drawn from the center of the circle to the point of tangency of the tangent BC, then this segment is perpendicular to the tangent BC, and then the angle OAB = OAC = 90, and the triangles OAB and OAC are rectangular.

In right-angled triangles ОАВ and ОАС, the hypotenuse ОВ = ОС by condition, the leg ОА is common in construction, then triangles ОАВ and ОАС are equal according to the fourth sign of equality of right-angled triangles, according to the leg and hypotenuse.

Then AB = AC = 6 cm.

Answer: The length of the segment AB is 6 cm.

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