To find the radius of the circle, we can use the properties of tangents and right triangles.
Given:
- The lengths of the tangents BC and BD are both 4 cm.
- The distance AB is 5 cm.
Since tangents drawn from a point outside a circle to the circle are equal in length, we know that BC = BD = 4 cm.
Triangle ABC is a right triangle where:
- AC is the radius of the circle (which we need to find).
- AB is the distance from point A (the center) to point B (the point outside the circle) which is 5 cm.
- BC is the tangent from point B to point C, which is 4 cm.
According to the Pythagorean theorem: \[ AB^2 = AC^2 + BC^2 \]
Substituting the known values: \[ 5^2 = AC^2 + 4^2 \] \[ 25 = AC^2 + 16 \]
Now, solving for \( AC^2 \): \[ AC^2 = 25 - 16 \] \[ AC^2 = 9 \]
Taking the square root: \[ AC = \sqrt{9} \] \[ AC = 3 \]
Therefore, the radius of the circle is 3.