Sure, let's solve this step by step!
First, let's find the length of the tangents. We can use the Pythagorean theorem to do that. The distance from the center of the circle to the point of tangency is 3 m. The distance from the external point to the center of the circle is 6 m.
Using the Pythagorean theorem, we can calculate the length of the tangents:
Length of tangents = √(Distance from center to point of tangency)^2 - (Radius)^2
Length of tangents = √(6^2 - 3^2)
Length of tangents = √(36 - 9)
Length of tangents = √27
Length of tangents = 3√3 m
Now, let's move on to the second part of the question. The angle between a radius to the point of tangency and the line joining the center of the circle to the point outside the circle is given as 60°.
The angle between the two tangents from the external point is always twice the angle between the radius and the line joining the center to the point outside the circle.
So, the angle between the two tangents is 2 * 60° = 120°.
Hope that helps! Let me know if you have any more questions.