Secant Line Of A Circle

A line that intersects a circumvolve in exactly 1 point is chosen a tangent and the signal where the intersection occurs is called the indicate of tangency. The tangent is e'er perpendicular to the radius drawn to the signal of tangency.

tangent radius secant

A secant is a line that intersects a circle in exactly 2 points.

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

Circle Two Secants

$$g\angle A=\frac{1}{2}(m\overline{DE}-m\overline{BC} )$$

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:

Circle Two Chords

$$AB\cdot EB=CE\cdot ED$$

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

Circle Two Secants

$$AB\cdot AD=Air-conditioning\cdot AE$$

If one secant and ane tangent are drawn to a circle from one outside signal, then the square of the length of the tangent is equal to the production of the external secant segment and the total length of the secant:

Circle Secant Tangent

$$AB^{two}=AC\cdot AD$$

If we have a circle drawn in a coordinate plane, with the eye in (a,b) and the radius r and then we could always describe the circle with the following equation:

$$(x-a)^{ii}+(y-b)^{ii}=r^{2}$$