From a point A outside a circle with centre O, a tangent AB is drawn to the circle. The circle's radius measures 6 cm, and the tangent segment AB has a length of 8 cm. Find the distance between point A and the centre O of the circle.
10 cm
A tangent to a circle is perpendicular to the radius drawn to the point of contact, so \(OB \perp AB\) where B is the point of contact.
Therefore triangle OBA is right-angled at B, with OB the radius and AB the tangent.
Here the radius \(OB = 6\) cm and the tangent \(AB = 8\) cm.
By the Pythagoras theorem, \(OA^2 = OB^2 + AB^2\).
Substituting: \(OA^2 = 6^2 + 8^2 = 36 + 64 = 100\).
So \(OA = \sqrt{100} = 10\) cm.
The distance between point A and the centre O is 10 cm.
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