Let A, B, C, D be four distinct points on a line, in that order. The circles with diameters AC and BD intersect at X and Y. Let P be a point on the line XY such that P¢ BC. The line CP intersects the circle with diameter AC at C and M, and the line BP intersects the circle with diameter BD at B and N. Prove that the lines AM, DN and XY are concurrent.

Let A, B, C, D be four distinct points on a line, in that order. The circles with diameters AC and BD intersect at X and Y. Let P be a point on the line XY such that P¢ BC. The line CP intersects the circle with diameter AC at C and M, and the line BP intersects the circle with diameter BD at B and N. Prove that the lines AM, DN and XY are concurrent.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.2: Length And Angle: The Dot Product

Problem 6AEXP

See similar textbooks

Similar questions

Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then _. b If ab and bc, then _.
In Exercises 11 to 14, find the distance between the two points P1 and P2. P1=0,0,0 and P2=1,2,4
X, Y, and Z are on circle O such that mXY=120, mYZ=130, and mXZ=110. Suppose that triangle XYZ is drawn and that the triangle ABC is constructed with its sides tangent to circle O at X, Y, and Z. Are XYZ and ABC similar triangles?
In trapezoid RSTV of Exercise 13, RSVT and MN is the median, Find x if VT=2x+9,MN=6x13,andRS=15. Exercise 13, 14
Show construction lines and arcs for each of these exercises. Trace each line segment in Exercises a through d and construct perpendicular bisectors to each segment.
Given: mn Transversal k m3=x23x m6=(x+4)(x5) Find: x and m4 Exercise 17-19
Describe the auxiliary line segment as determined, overdetermined, or underdetermined. a) Through vertex B of ABC, draw ABAC. b) Draw the line that contains A, B, and C. c) Draw the line that contains M, the midpoint of AB.
Let A, B, and C lie on a straight line as shown near Exercise 8. Classify these claims as true or false. a B lies between A and C. b AB is a ray with endpoint B.