Question

the length of a tangent from a point A at distance 5 cm from the centre of a circle is 4 cm . find radius of a circlce

Answer 1

r^2+4^2=5^2

r^2=25-16

r=3

Answer 2

Let the center be O and point of contact of tangent with circle be B.
Then, ABO is a right angle triangle
OB is the radius
Given, AB = 4, OA = 5
${AB}^{2} + {OB}^{2} = {OA}^{2} \\ radius \: \: OB = \sqrt{ {5}^{2} - {4}^{2} } = 3 \: cm$