Q1 of 31 Page 218

An external point is situated at a distance of 17 cm from the centre of a circle having 16 cm. diameter, let us determine the length of the tangent drawn to the circle from the external point.

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Let O be the centre, B be the external point and A be the point where the tangent meets the circle.


OA is the radius of the circle


Diameter = 16 cm


Radius = OA = 8 cm


OB = 17 cm


Δ AOB is a right angled triangle with ∠ A = 900


Applying Pythagoras theorem :


AB2 = AO2-OB2


⇒ AB2 = 172-82


⇒ AB2 = 289-64


⇒ AB2 = 225


⇒ AB = 15 cm


The length of the tangent drawn to the circle from the external point is 15 cm


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