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
Hence, Radius = 3 cm