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Circle: Tangents
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Circle: Tangents
A line or line segment that touches the perimeter of a circle at one point only and is perpendicular to the radius that contains the point is called tangent of a circle i.e. it intersects the circle's radius at 90angle.
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Example: The string of a kite is 50 meters long and it makes an angle of 60 with the horizontal, find the height of the kite, assuming that there is no slack in the string.
Solution: Let OA be the horizontal ground, and let B be the position of the kite at a height h above the ground. Then, AB = h. It is given that OB = 50 meters and AOB = 60.
In AOB, we have sin 60 = AB/OB
sin 60 = h/100
h = 50 sin 60
h = 50(3/2) = 253 = 43.30 metres
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