2 + y2) is π/2 (90 degrees).

Explanation:

Let's start by finding the equation of the circle.

x2 + y2 = r2

where r is the radius of the circle. Since the circle passes through the origin, we know that the radius is equal to the distance from the origin to any point on the circle.

r = √(x2 + y2)

So the equation of the circle can be rewritten as:

x2 + y2 = ( √(x2 + y2) )2

Simplifying, we get:

x2 + y2 = x2 + y2

0 = 0

This is a true statement, which means that any point (x, y) that satisfies the equation x2 + y2 = r2 lies on the circle.

Now let's draw the tangents from the origin to the circle.

We know that the tangent to a circle is perpendicular to the radius at the point of tangency. Since the origin is the center of the circle, the radius drawn to the point of tangency will be perpendicular to the tangent.

Therefore, the angle between the tangents drawn from the origin to the circle is equal to the angle between the radii drawn from the origin to the points of tangency.

Let (a, b) and (-a, -b) be the points of tangency. Then the radii drawn from the origin to these points are:

r1 = √(a2 + b2)

r2 = √((-a)2 + (-b)2) = √(a2 + b2)

So the angle between the radii is:

θ = cos-1 [(a(−a) + b(−b))/(r1r2)]

θ = cos-1 [(-a2 - b2)/(r1r2)]

θ = cos-1 (-1)

θ = π

This means that the angle between the radii (and hence the tangents) is π radians, or 180 degrees.

However, we need to find the angle between the tangents drawn from the origin to the circle, not the angle between the radii.

Since the tangents are perpendicular to the radii, the angle between the tangents will be 90 degrees less than the angle between the radii.

So the angle between the tangents is:

90 degrees = π/2 radians.