The length of the tangent from a point A at a circle, of radius 3 cm, is 4 cm. The distance of A from the centre of the circle is
Given:
AB (say) = 4 cm
Radius (OB) = 3 cm
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 ∠ABO.
Therefore,
By Pythagoras Theorem in ∆POQ,
OA2 = OB2 + BA2
⇒ OA= √(OB2 + BA2)
⇒ OA= √(32 + 42)
⇒ OA= √(9 + 16)
⇒ OA = √25 cm
⇒ OA = 5 cm
Hence, distance of A from center = 5 cm
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