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Question
In the given figure, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.
Solution
Here, AC and AB are the tangents from external point A to the smaller circle.
∴ AC = AB
Now, AB is the chord of bigger circle and OQ is the perpendicular bisector of chord AB.
∴ AQ = QB
or, AB = 2AQ
or, AB = 2(5) = 10 cm ...[∵ Given AQ = 5 cm]
or, AC = 10 cm
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