A tangent is a line that just skims the surface of a circle. It hits the circle at one point only. A tangent line of a circle will always be perpendicular to the radius of that circle. Questions that deal with this theorem usually go hand in hand with the Pythagorean theorem. Example If two tangents to the same circle share a point outside of the circle, then the two tangents are congruent.

These lines are equal as well. This free worksheet contains 10 assignments each with 24 questions with answers. Example of one question:. Terms of Use Privacy Policy. There are two main theorems that deal with tangents.

Find x. Since both lines are tangents and share the point B, then they are equal.

**TANGENT LINES AND CIRCLES EXPLAINED!**

Example 3: All lines are tangents. Find the perimeter of the polygon. We have to determine which lines are equal. They have to be tangents that hit the same point. Example 4: All lines are tangents. This one is a little bit tougher.

We have to figure it out piece by piece.

### Circles, arcs, chords, tangents ...

Add all the sides. Determine if line AB is tangent to the circle. Example of one question: Watch bellow how to solve this example:. Find the perimeter of each polygon. Assume that lines which appear to be tangent are tangent. Solve for x. Algebra and Pre-Algebra. Back to Top.Tangent to a Circle Theorem: A tangent to a circle is perpendicular to the radius drawn to the point of tangency. A straight line that cuts the circle at two distinct points is called a secant.

Example :. In the following diagram a state all the tangents to the circle and the point of tangency of each tangent. Solution :. AB is a tangent to the circle and the point of tangency is G. CD is a secant to the circle because it has two points of contact. EF is a tangent to the circle and the point of tangency is H. The two-tangent theorem is also called the "hat" or "ice-cream cone" theorem because it looks like a hat on the circle or an ice-cream cone.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. Scroll down the page for more examples and solutions.

Tangent to a Circle A tangent to a circle is a straight line, in the plane of the circle, which touches the circle at only one point.

The point is called the point of tangency or the point of contact. What is the tangent of a circle? A tangent is a line in the plane of a circle that intersects the circle at one point. The point where it intersects is called the point of tangency. Show Step-by-step Solutions.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.In the following diagram, PA and PB are tangents to the circle. Find the value of:. Solution :. Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page. In this lesson, we will look at finding angles in diagrams that involve tangents and circles. Some of the theorems used are: Tangent to Circle Theorem Pythagorean Theorem Two-Tangent Theorem The following diagram shows the properties of the line segments and angles formed by the tangents from a point outside a circle.

Scroll down the page for more examples and solutions on how to use the properties to solve for angles. You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Circle Cal on its own page.

Status: Calculator waiting for input. More interesting math facts here! To solve this probelm, you must remember how to find the meaure of the interior angles of a regular polygon.

Use the inscribed angle formula and the formula for the angle of a tangent and a secant to arrive at the angles. Home Geometry Circles.

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Theorems involving Angles and Arcs.

Theorems involving Segments tangents, secants. Product of Segments heorem.The three theorems for the intercepted arcs to the angle of two tangents, two secants or 1 tangent and 1 secant are summarized by the pictures below. If you look at each theorem, you really only need to remember ONE formula. The angle formed by the intersection of 2 tangents, 2 secants or 1 tangent and 1 secant outside the circle equals half the difference of the intercepted arcs!

Therefore to find this angle angle K in the examples belowall that you have to do is take the far intercepted arc and near the smaller intercepted arc and then divide that number by two!

All of the formulas on this page can be thought of in terms of a "far arc" and a "near arc". The angle formed outside of the circle is always equal to the the far arc minus the near arc divided by 2. Remember that this theorem only used the intercepted arcs. Therefore, the red arc in the picture below is not used in this formula. The measure of an angle formed by a 2 secants drawn from a point outside the circle is half the the difference of the intercepted arcs:.

Remember that this theorem only makes use of the intercepted arcs. Therefore, the red arcs in the picture below are not used in this theorem's formula. In one way, this case seems to differ from the others-- because all circle is included in the intercepted arcs. Since both of the lines are tangents, they touch the circle in one point and therefore they do not 'cut off' any parts of the circle.

Applet on its own page. Only one of the two circles below includes the intersection of a tangent and a secant. What is the measure of x in the picture on the left. Both lines in the picture are tangent to the circle.

Two secants extend from the same point and intersect the circle as shown in the diagram below. What is the value of x? Use your knowledge of the theorems on this page to determine at whether point C or point D is where the bottom segment intersects the circle. In other words, is point D tangent to the circle? Worksheet with answer key on this Topic. Circle Theorems. Interactive app. Show Answer. Can you figure out which one? Both lines in the picture are tangent to the circle Show Answer.

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## Tangents, Secants, Arcs and Angles

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### Tangents of circles problems

When you start teaching your unit on Circles, Tangent Lines, and Secant Lines there are a lot of vocabulary words that your students will need to learn. One of the best ways to teach Vocabulary is with a good graphic organizer. We created a graphic organizer for you to use with them. You can download it in the Freebie section at the bottom of this post! Here is your free content for this lesson on Tangent Lines! Don't Forget to Pin This Lesson! One Comment Definitely, using this GO for my class as we start circle theorems.

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