Download presentation

1
**Properties of Tangents of a Circle**

Adapted from Walch Education

2
tangent line A tangent line is a line that intersects a circle at exactly one point. Tangent lines are perpendicular to the radius of the circle at the point of tangency. 3.1.3: Properties of Tangents of a Circle

3
**Key Concepts, continued**

You can verify that a line is tangent to a circle by constructing a right triangle using the radius, and verifying that it is a right triangle by using the Pythagorean Theorem. The slopes of a line and a radius drawn to the possible point of tangency must be negative reciprocals in order for the line to be a tangent. If two segments are tangent to the same circle, and originate from the same exterior point, then the segments are congruent. 3.1.3: Properties of Tangents of a Circle

4
circumscribed angle The angle formed by two tangent lines whose vertex is outside of the circle is called the circumscribed angle. ∠BAC in the diagram is a circumscribed angle. The angle formed by two tangents is equal to one half the positive difference of the angle’s intercepted arcs. 3.1.3: Properties of Tangents of a Circle

5
secant line A secant line is any line, ray, or segment that intersects a circle at two points. An angle formed by a secant and a tangent is equal to the positive difference of its intercepted arcs. 3.1.3: Properties of Tangents of a Circle

6
Practice Each side of is tangent to circle O at the points D, E, and F. Find the perimeter of . 3.1.3: Properties of Tangents of a Circle

7
**Solution Identify the lengths of each side of the triangle.**

is tangent to the same circle as and extends from the same point; therefore, the lengths are equal. AD = 7 units 3.1.3: Properties of Tangents of a Circle

8
Solution, Continued is tangent to the same circle as and extends from the same point; therefore, the lengths are equal. BE = 5 units To determine the length of , subtract the length of from the length of 16 – 5 = 11 CE = 11 units 3.1.3: Properties of Tangents of a Circle

9
Solution, continued is tangent to the same circle as and extends from the same point; therefore, the lengths are equal. CF = 11 units 3.1.3: Properties of Tangents of a Circle

10
**And Finally! Calculate the perimeter of**

Add the lengths of to find the perimeter of the polygon. = 46 units The perimeter of is 46 units. 3.1.3: Properties of Tangents of a Circle

11
**Your turn… is tangent to at point B as shown at right.**

Find the length of as well as 3.1.3: Properties of Tangents of a Circle

12
Thanks for Watching! ~ms. dambreville

Similar presentations

OK

Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

Circle. Circle Circle Tangent Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on main festivals of india Lecture ppt on digital image processing Ppt on 7 wonders of the modern world Ppt on area related to circles for class 10 Marketing management ppt on jeans Ppt on geography of india Ppt on fdi policy in india Ppt on company act 2013 Ppt on total parenteral nutrition solutions Ppt on e-commerce websites