Q. 125.0( 1 Vote )

# In the given figure, AB and AC are tangents to a circle with center 0 and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) isA. 9B. 15C. 353D. 25

As AB is tangent to the circle at point B

OB AB

[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]

In right angled triangle AOB,

By Pythagoras Theorem,

[i.e. (Hypotenuse)2 = (Base)2 + (Perpendicular)2 ]

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

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

[As OA = 17 cm is given and OB is radius]

289 = 64 + (AB)2

(AB)2 = 225

AB = 15 cm

Now, AB = AC [Tangents drawn from an external point are equal]

AC = 15 cm

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