The length of a tangent drawn to a circle of radius 4 cm from a point 5 cm away from the center of the circle is:

Correct option is D

Given:

The length of a circle of radius = 4 cm

Distance from the center of the circle to the external point = 5 cm 

Formula Used:  

Tangent to the circle make right angle with the center.

In the Pythagorean theorem = $$H^2 = P^2 + B^2$$ 

Solution:

According to the given figure, 

According to the question,

We get,

​$$H^2 = P^2 + B^2 \\ \ \\ BC^2 =AB^2 + AC^2 \\ \ \\ 5^2 = 4^2 + AC^2 \\ \ \\ AC^2 = 25 - 16 \\ \ \\ AC = \sqrt 9 = 3$$  

Thus, The tangent AC = 3cm