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 cm
(b) 15 cm
(c) $\sqrt{353} \mathrm{~cm}$
(d) 25 cm
Solution:
We know that the radius and tangent are perperpendular at their point of contact
In right triangle AOB
By using Pythagoras theorem, we have
OA2 = AB2 + OB2
⇒ 172 = AB2 + 82
⇒ 289 = AB2 + 64
⇒ AB2 = 225
⇒ AB = 15 cm
The tangents drawn from the external point are equal.
Therefore, the length of AC is 15 cm
Hence, the correct answer is option (b).
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