Q1 of 35 Page 11

The length of a tangent from a point A at a distance 5cm from the centre of a circle is 4cm. Find the radius of the circle.

Let the centre of circle be O so that AO = 5 cm


Tangent is AB whose length is 4 cm


OB is radius as shown



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


⇒ 42 + OB2 = 52


⇒ 16 + OB2 = 25


⇒ OB2 = 25 – 16


⇒ OB2 = 9


⇒ OB = ±3


As length cannot be negative


⇒ OB = 3 cm


Hence length of radius is 3 cm


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