Question

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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.

Answer 1

`AB=12√(3)\ cm`

Explanation:

If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special
`30^(\circ)-60^(\circ)-90^(\circ)` triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,

`AO=2BO=2\cdot 12=24\ cm.`

By the Pythagorean theorem,

`AB^2=AO^2-BO^2,\\ \\AB^2=24^2-12^2,\\ \\AB^2=576-144=432,\\ \\AB=12√(3)\ cm.`