Tangent of a Circle
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Tangent of a Circle
A tangent to a circle is a line that intersects the circle in exactly one point.
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Example: Find the length of the tangent drawn from a point whose distance from the center of a circle is 7 cm. Given that the radius of the circle is 5 cm.
Solution: Let A be the given point, O be the centre of the circle and AT be the length of tangent from A. Then, OA = 7 cm and OT = 5 cm.
Since tangent to a circle is always perpendicular to the radius through the point of contact.
Therefore, OTA = 90 degree

In right triangle OTA, we have
OA2 = OT2 + AT2
72 = 52 + AT2
 AT2 = 72- 52 = (7 - 5) ( 7 + 5) = 24
AT = 26 cm
Hence, length of tangent from A = 26 cm.

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