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.

Answer 1

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