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Tangent Perpendicular to Radius at Point of Contact

In the given ...

Question

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is

(a) 9 (b) 15 (c) $\sqrt{353}$ (d) 25

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Solution

given,

OA = 17 cm

OB = 8 cm

by pythagoras theorem,

$A B^{2} + O B^{2} = O A^{2}$

$A B^{2} = 289 - 64$

$A B^{2} = 225$

AB = 15

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