Q3 of 35 Page 11

Find the length of the tangent drawn from a point, whose distance from the centre of a circle is 5c, and the radius of the circle is 3 cm.

Let A be the point at distance of 5 cm from the centre as AO = 5 cm


AB is the tangent at point B as shown


OB is the radius which is 3 cm



Now we know that radius is perpendicular to point of contact


Hence OB is perpendicular to AB


Hence ∠ABO = 90°


Consider ΔABO


Using Pythagoras theorem


⇒ AB2 + OB2 = AO2


⇒ AB2 + 32 = 52


⇒ AB2 + 9 = 25


⇒ AB2 = 25 – 9


⇒ AB2 = 16


⇒ AB = ±4


As length cannot be negative


⇒ AB = 4 cm


Hence length of tangent is 4 cm


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