Question

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

Answer 1

The radius of the circle is 3 cm.

Step-by-step explanation:

Refer the attached diagram, the circle with centre O. In that given, AB is tangent given as 4 cm and distance of point from the circle, OA = 5 cm

As AB is tangent, OB (radius of circle) is perpendicular to AB (tangent at any point of circle). Therefore the angle of OBA is 90 degree.

Also, triangle OAB is a right angled triangle (refer attached diagram). By using Pythagoras theorem in right angled triangle,

             $(\text {Hypotenuse})^{2}=(\text {Height})^{2}+(\text {Base})^{2}$

             $(O A)^{2}=(O B)^{2}+(A B)^{2}$

Substitute the given values in the above expression, we get

             $(5)^{2}=(O B)^{2}+(4)^{2}$

             $(O B)^{2}=25-16=9$

Taking square root on both side, we get

              Radius of the circle, OB = 3 cm