Question 10

The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cms. Radius of the circle is

Solution

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Here, AB is tangent of the circle with centre O.
OA is the distance of A from centre O.
$$\triangle$$ OAB is a right angled triangle right angled at B.
$$OA^2 = AB^2 + OB^2$$
=> $$5^2 = 4^2+OB^2$$
=> $$25 = 16+OB^2$$
=> $$OB^2 = 9 => OB = 3$$
Therefore, Radius of the circle = 3 cm.

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