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A circle k(O) with the radius r is given. Line AB tangent to circle k(O) at B. Find AB, if m∠AOB=60°, and r=12 cm.

If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex] triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,

[tex]AO=2BO=2\cdot 12=24\ cm.[/tex]

By the Pythagorean theorem,

[tex]AB^2=AO^2-BO^2,\\ \\AB^2=24^2-12^2,\\ \\AB^2=576-144=432,\\ \\AB=12\sqrt{3}\ cm.[/tex]

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HELP IN NEED! A circle k(O) with the radius r is given. Line AB tangent to circle k(O) at B. Find AB, if m∠AOB=60°, and r=12 cm.

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HELP IN NEED!
A circle k(O) with the radius r is given. Line AB tangent to circle k(O) at B. Find AB, if m∠AOB=60°, and r=12 cm.