25+Secants+and+Tangents+(Inside,+Outside,+On)

Summary: First of All: What is a secant and what the heck is a tangent?

A **secant** is a line that intersects a curve of a circle on TWO different points.

A **tangent** is also a line that intersects at ONLY ONE point on the curve of a circle. This line is an external line, passing through ONE point on the circle.


 * Remember that segments drawn within, through, or tangent to a circle creates angels.

This is to help teach you: The BASIC FORMULA that deals with secants and tangents are based off what is above. In order to set up an equation properly, you must understand and recognize which arcs to plug in. This always pertains the to the angle formed OUTSIDE OF THE CIRCLE.

You can see that there is a tangent line intersecting the circle at one point and then there is a secant line intersecting at two points on the circle. Together they form an angle outside of the circle. In this case it is K, as seen above. The next one shows two secants intersecting to form K. Finally, there is a a picture showing two tangent lines intersecting to form K.

This clearly shows you which arcs to plug into the equation and by doing this, you will be able to figure out any problem given to you.!=) Remember this equations only pertains to ANGLES FORMED OUTSIDE OF THE CIRCLE b either a tangent and a secant, two tangents, or two secants!

This shows a tangent line and a secant forming an angle K. This shows two tangent lines intersecting to form angle X. Finally, this shows two secant lines intersecting to form X.

NOW REMEMBER THERE ARE OTHER ANGLES THAT ARE FORMED THAT DO NOT NECESSARILY INTERSECT OUTSIDE THE CIRCLE.

Here fr instance, This shows how the tangent line and the chord of the circle intersected to form an angle ON the circle. TO find this angle, you must find half of its intercepted arc! Simple as that!

FINALLY when there is an intersection in the circle, the formula to find its measurement is quite the same as the other. They are otherwise known as inscribed angel, like the other example above.

Above, you can see how the angle is inside the circle. This just shows how the angles is half the intercepted arc.

NOW YOU KNOW ALL ABOUT TANGENTS AND SECANTS AND HOW TO FIND THEIR ANGLE MEASURES!

Just remember that you have to use your head and determine if the lines are intersecting inside, on, or outside of the circle. This then will let you know how to find the particular angle that you are asked. Look, Think, and you'll be fine. Determine the correct arcs to use and then continue from there !

PRACTICE:

1) answer 1

Question 2: answer 2

question 3: answer 3



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