Q. 14.7( 24 Votes )

Find the length of tangent drawn to a circle with radius 8 cm from a point 17 cm away from the center of the circle.

Answer :

Let us consider a circle with center O and radius 8 cm.


The diagram is given as:



Consider a point A 17 cm away from the center such that OA = 17 cm


A tangent is drawn at point A on the circle from point B such that OB = radius = 8 cm


To Find: Length of tangent AB = ?


As seen OB AB


[Tangent at any point on the circle is perpendicular to the radius through point of contact]


In right - angled ΔAOB, By Pythagoras Theorem


[i.e. (hypotenuse)2 = (perpendicular)2 + (base)2 ]


(OA)2 = (OB)2 + (AB)2


(17)2 = (8)2 + (AB)2


289 = 64 + (AB)2


(AB)2 = 225


AB = 15 cm


The length of the tangent is 15 cm.


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