Question

Given: OA = AC = 2
AB is a tangent line to k(O)

Find: AB

Answer 1

• AB = 2√3 units

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Tangent is perpendicular to radius, hence ΔAOB is right triangle.

Given that OA = AB, and we know OA = OC as two radius. Therefore OAC is equilateral triangle, hence all its angles are same:

• m∠AOC = 180°/3 = 60°

It means ΔOAB is a specific 30x60x90 right triangle.

The ratio of its sides is:

• OA : AB : OB = 1 : √3 : 2

It gives us that:

• AB = OA√3
• AB = 2√3