A tangent and a secant are drawn from the point A, which is outside the circle. AB = 6, AC = 4. Find the length of the line segment AD.
Let’s build the chords BC and BD. Consider the triangles ABD and ABC.
The angle C is common for the triangles.
Angle ADC = ABC by the property of inscribed angles. Then triangles ABD and ABC are similar in two angles.
In similar triangles: AB / AD = AC / AB.
AB ^ 2 = AD * AC.
36 = 4 * AD.
AD = 36/4 = 9 cm.
Answer: The length of the segment AD is 9 cm.
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