# The length of tangent from a point A at a distance of 5 cm from the center of the circle is 4 cm. What is the radius of the circle?

Given:

OA (say) = 5 cm

AB = 4 cm

Let AC be the tangent which meets the circle at the point B and O be the center of circle.

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆AOB is right-angled at OBA.

Therefore, by Pythagoras Theorem,

AB2 + OB2 =AO2

OB 2 = AO2 – AB2

OB= √(AO2 – AB2)

OB= √(52 – 42)

OB= √(25 – 16)

OB = √9

OB= 3 cm

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