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) is

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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