The length of a tangent from a point A at a d | vedclass

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(B) Let the centre of the circle be $O$ and the point from which the tangent is drawn be $A$.Let $B$ be the point of contact of the tangent on the cir

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$3$

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(B) Let the centre of the circle be $O$ and the point from which the tangent is drawn be $A$.Let $B$ be the point of contact of the tangent on the circle.Given that the distance of point $A$ from the centre $O$ is $OA = 5 \, cm$.The length of the tangent $AB = 4 \, cm$.We know that the radius of a circle is perpendicular to the tangent at the point of contact.Therefore,$OB \perp AB$,which makes $	riangle ABO$ a right-angled triangle with $\angle OBA = 90^\circ$.Applying the Pythagoras theorem in $	riangle ABO$:$OA^2 = AB^2 + OB^2$$5^2 = 4^2 + OB^2$$25 = 16 + OB^2$$OB^2 = 25 - 16$$OB^2 = 9$$OB = \sqrt{9} = 3 \, cm$.Thus,the radius of the circle is $3 \, cm$.

The length of a tangent from a point $A$ at a distance of $5 \, cm$ from the centre of the circle is $4 \, cm$. Find the radius of the circle. (in $, cm$)

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