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Related sites Secant Lines

Geometry Circles: Tangent lines and Secant Lines/Sparknotes   This site reviews tangent lines and secant lines and includes pictures. Sparknotes does a good job of keeping the definitions and explanations of these Geometry terms brief, and easy to understand.

Circles: Secants and Tangents  This page created by AlgebraLAB explains how to measure and define the angles created by tangent and secant lines in a circle.

Rules for Dealing with Chords, Secants, Tangents in Circles  This page created by Regents reviews three rules that are used when working with secants, and tangent lines of circles.
When two secants intersect
When two secants intersect When two secants intersect When two secants intersect
When two secants intersect
secant line  is a line that intersects and passes through a curve or circle at two or more points.

tangent line is a line that intersects a curve or circle at one point.
The point of tangency is the point where the curve or circle intersects the tangent line.

Step 1. The measure of the big arc will be from wx in the picture and the small arc will be from yz

(Big Arc- Small Arc) ⁄ 2 

(80°-20°) ⁄ 2 

(60°) ⁄ 2 = 30°


Hi Welcome to MooMooMath. Today we are going to look at angles created by secants. We are looking at secant sections. Now a secant is a line that through a circle in two places. So we have this line (points to line A Y) is a secant segment and A X is a secant segment and we have angle A outside the circle. We need to find the measure of that angle A Now there is a neat little formula that you can learn to find that angle measure. Now what you are doing is looking inside the mouth. Now if this is a mouth we have two arcs. We have a small arc and we have a large arc. If I refer to small arc I’m refereeing to this smaller arc inside the mouth and this larger one (points to top, larger arc.) We are going to take the big arc which is 120 in this case minus the small arc and take the difference and divide by two. So let’s plug in some numbers. The larger arc is 120 the smaller arc is forty. I’m going to subtract those to get 80 and I’m going to divide by two. This angle A is forty degrees. Now this angle is just happened to be the same as the arc. This is not typical so don’t think you just take the arc and stick it down there. You have to subtract and divide by two, but that is how you find the angle. Let’s look at the rules for finding angles created by secants. Take the big arc minus the small arc divide by two in order to get the angle measure. Here is a second example of that. We are going to take arc WX the large arc minus YZ the small arc and divide by two. I have replaced WX with 80 minus 20 and divide by two. So take 60 divided by two so angle 1 out here is 30 degrees. Hope this video was helpful

secant to a circle

Secant Line

Angle A
The big arc is from W to X and measures 80 degrees
The small arc is from Z to Y  and the angle measure is 20 degrees
Let's look at a sample problem.

Find the measure of the exterior angle A created by two secant lines, if the big arc measures 80 degrees, and the small arc measures 20 degrees.
Step 2. Plug your numbers into the formula and solve
Example 2  Find the angle measure of the exterior angle A created by two secant lines, if the big arc measures 120 degrees, and the small arc measures 40 degrees.
secant to a circle
Step 1. Use the formula (Big Arc- Small Arc) ⁄ 2 

Step 2. Plug in your numbers (120°-40°) ⁄ 2 

Step 3. Solve  80° ⁄ 2 = 40° =Angle A

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Angles created by secants explained

Secant Lines

secant line
secant line
line intersects two points/secant line
Test yourself, Is the picture a secant line or a tangent line? Roll over the picture for the answer.
secant line
tangent line
When two secant lines intersect outside of a circle they form an angle on the exterior of the circle. To find the measure of the exterior angle, you need to know the measure of the two intercepted arcs. Those arcs fall between the two secants. One is large and one is small. To find the exterior angle, use the formula, big arc - small arc divided by 2. 

Segment Rules of Circles Involving Secant Lines

secent secant rule
secant tangent rule
Secant Secant Rule:  Using the same external point, if two secant segments are drawn, the sum of one secant segment, and it's external part is equal to the sum of the other secant segment and it's external part
                     a*b =c*d

whole secant * external part = whole secant * external part
Secant Tangent Rule: If drawn from the same point, the sum of the secant segment, and its external part equals the square of the tangent segment.

b * c = a^2

whole secant*external part = tangent squared