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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 ______.
Options
9
15
`sqrt(353)`
25
MCQ
Fill in the Blanks
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Solution
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 15.
Explanation:
Draw OC to the point of contact C.
OC = 8 is perpendicular to tangent AC, so triangle OCA is right-angled.
By Pythagoras, `AC = sqrt(OA^2 - OC^2)`
= `sqrt(17^2 - 8^2)`
= `sqrt(289 - 64)`
= `sqrt(225)`
= 15
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