In an isosceles triangle ABC (AC = BC), where BE is the altitude and EC is the diameter of the circle with center O. If AD is tangent to the circle and measures 10, calculate the length of AB.

**Problem 1539**

Geometry's dance,

Isosceles triangle's stance,

Altitude and tangent,

Unveil secrets persistent,

Length of AB, sought and revealed.

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Triangle

Isosceles Triangle

Right Triangle

Altitude

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Diameter

Tangent

Midpoint

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