Answer: 35 cm
Step-by-step explanation:
Given : Diameter of a circle= 24 cm
Let r be the radius of the circle.
then [tex]r=\frac{d}{2}=12\ cm[/tex]
Since a tangent is always at right angles to the radius where it touches the circle.
Join the point A to the center of the circle such that it will become a right triangle with 37 cm as the longest sides [since it is the side opposite to the right angle.]
Let x denote the length of the tangents.
By Pythagoras theorem, we have
[tex]r^2+x^2=(37)^2\\\Rightarrow\ (12)^2+x^2=1369\\\Rightarrow\ x^2=1369-144\\\Rightarrow\ x^2=1225\\\Rightarrow\ x=35[/tex]
Hence, the length of each tangent from point a to the point of the tangency=35 cm
