In a circle, the perpendicular bisector of a chord contains the center of the circle.Given: OX with L the bisector of WY.Prove: L contains the center of OX.Statements1.Connect points X and W and X and Y to form▼2.3.X is on the bisector of4.X is on ▼5 L contains the center of OX(…)WXY1. Construction2. All radii of a circle are3. Converse of the Bisector Theorem4. Substitution5.Reasons

Converse of perpendicular bisector theorem : if a given point is equidistant to the end the points…

Answered: In a circle, the perpendicular bisector…

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 28E

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Similar questions

Given that mAC:mBC:mAB=4:3:2 in circle O: a Which arc is largest? b Which chord is longest?
aBecause point Q is their common center, these circles are known as _ circles. bIf RQ=3 and QV=5, find the length of chord TV which is also a tangent to the inner circle.
Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle.
For compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the boards upper surface to be parallel to the ground when the wheels are dropped, what relationship must exist between AB and CD?
Note: Exercises preceded by an asterisk are of a more challenging nature. In the figure, which of the points E,F,G,H, and K belong to the locus of points in the plane that are at distance r from line l?
The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent AB? HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.
In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._
Note: Exercises preceded by an asterisk are of a more challenging nature. In the figure, which of the points A,B,C,D, and E belong to the locus of points in the plane that are at distance r from point P?
For compactness, the drop-down legs of an ironing board fold up under the board. A sliding mechanism at point A and the legs being connected at common midpoint M cause the boards upper surface to be parallel to the floor. How are AB and CD related?
In the drawing, ABDCEF with transversals l and m. If D and C are the midpoints of AE and BF, respectively, then is trapezoid ABCD similar to trapezoid DCFE?
Refer to the prisms of Exercises 1 and 2. Which of these have symmetry with respect to one or more planes?
Prove the statements in Review Exercises 32 to 36 using analytic geometry. If the diagonals of a trapezoid are equal in length, then the trapezoid is an isosceles trapezoid.

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