CK12 - Geometry

d. and Answers a. is a radius. b. is a diameter. c. is a tangent. d. is a secant. e. is a chord. f. is a radius. is congrue ...

16. 17. 18. 19. The centeris locatedat , radius=. The centeris locatedat , radius=. The centeris locatedat , radius=. ...

Tangentto a Circle Tangentto a CircleTheorem:A tangentline is alwaysat right anglesto the radiusof the circleat the pointof tang ...

Theremustbe anotherpoint on the tangentline suchthat is perpendicularto the tangentline. Therefore,in the right triangle , is th ...

feet in one mile.)How far can Marksee to the horizon? We start by drawingthe figureabove. The distanceto the horizonis givenby t ...

Proof. We will provethis theoremby contradiction.Sincethe line is perpendicularto the radiusat its outerendpoint it musttouchthe ...

The lengthsof the sidesof the trianglesatisfythe PythagoreanTheorem,so is perpendicularto and is thereforetangentto the circle. ...

Example 4 Find the perimeterof the triangle. All sidesof the triangleare tangentto the circle. The TangentSegmentsfrom a CommonE ...

and are both isoscelesright triangles,therefore and all the correspondingsidesare proportional: We can find the lengthof by usin ...

is a tangentto the circle is a tangentto the circle is the centerof the circle Prove Proof. We will use a similarfigureto th ...

This has a doubleroot at =. This meansthat the line intersectsthe circleat only one point. A perpendicularline to the tangentlin ...

c. Find the measureof angle. a. b. c. ...

Find the missinglength: a. b. c. ...

Find the valuesof the missingvariables a. b. c. ...

Find the perimeterof the pentagon: Find the perimeterof the parallelogram: Find the perimeterof the right triangle: Find the pe ...

Drawthe line = + and the circle + =. Showthat thesegraphstouchat only one point. Find the slopeof the segmentthat joins this p ...

6. 7. 8. solvefor to obtaindoubleroot. The slopeof the line from to , whichis the negativereciprocalof the slopeof the line. T ...

Let’s labelthe diagramand drawa line segmentthat joinsthe centersof the two circles.Also drawthe segment perpendicularthe radius ...

Tangentis perpendicularto the radius Tangentis perpendicularto the radius Both equal Verticalangles similaritypostulate Therefor ...

ExternallyTangentCircles Hereare someexamplesinvolvingexternallytangentcircles. Example 3 Circlestangentat are centeredat and . ...