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1

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.

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.