A line that intersects a circle in exactly one point is called a tangent and the point where the intersection occurs is called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency.

A secant is a line that intersects a circle in exactly two points.

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

mA = ½(mDE – mBC)

When two chords intersect inside a circle, then the measures of the segments of each

chord multiplied with each other is equal to the product from the other chord:

AB • EB - CE • ED

If two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal:

AB • AD •- AC • AE

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant:

AB2 - AC •AD

If we have a circle drawn in a coordinate plane, with the center in (a,b) and the radius r

then we could always describe the circle with the following equation:

(x - a)2 + (y - b)2 = r2

Video lesson: Find the value of t in the figure.

To see the solution look at the video in the next page.

Here we have this perfect circle and we have some specifically drawn lines here and we know from some advanced knowledge about circles that there’s a particular formula we can use to find this length t. So if we define this as b and this as a and we know these lengths then we can find t. Of course we could do it in the reverse order as well if we’re looking for b or a if we need t. So that formula looks like this t2 = (a+b)b . So we can just plug in a and b here and solve for t. So t2 equals 12 plus five which is 17, times b which is 5. So t2 equals 17 times 5 which is 85 and we can take the square root of that, so t equals the square root of 85 which is approximately equal to 9.2 and that just comes from this formula here.