the length of a tangent from a point a at a distance 5 cm from the centre of a circle is 4 centimetre find the radius of the circle
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AB is a tangent drawn on this circle from point A.

∴ OB ⊥ AB
OA = 5cm and AB = 4 cm (Given)
In ΔABO,
By Pythagoras theorem in ΔABO,
OA2 = AB2 + BO2
⇒ 52 = 42 + BO2
⇒ BO2 = 25 - 16
⇒ BO2 = 9
⇒ BO = 3
∴ The radius of the circle is 3 cm.

∴ OB ⊥ AB
OA = 5cm and AB = 4 cm (Given)
In ΔABO,
By Pythagoras theorem in ΔABO,
OA2 = AB2 + BO2
⇒ 52 = 42 + BO2
⇒ BO2 = 25 - 16
⇒ BO2 = 9
⇒ BO = 3
∴ The radius of the circle is 3 cm.
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Answer:
The radius of the circle is 3 cm.
Step-by-step explanation:
The figure has been uploaded below:
AB is a tangent drawn on this circle from a point A.
Therefore OB is perpendicular to AB
Given:
OA = 5cm
AB = 4 cm
The ΔABO is a right angled triangle.
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides"
Therefore,
In ΔABO,
OA²= AB²+BO²
∴5²=4²+BO²
∴BO²=25-16
∴BO² =9
∴BO = 3
Therefore, the radius of the circle is 3 cm.
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