Wednesday, July 11, 2018

Geometry Problem 1360: Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1360: Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps.

2 comments:

  1. let P be midpoint of AB, then Point P lies on circle C1. D,F,H and P are concyclic.
    Hence BD.BP=BF.BH,
    BD.BP=BD.BA/2=BM.BA, we have BM.BA=BF.BH hence A,M,F and H are concyclic.

    ReplyDelete
  2. https://photos.app.goo.gl/d3YiN6DXi7drQFN98

    Draw AE and CD and note that AE and CD are altitudes of triangle ABC
    Let AB cut circle C1 at the midpoint N of AB
    Circle C1 will pass thru D, E and N ( properties of 9 points circle)
    Power from B to circle C1
    P(B)= BF.BH= BD.BN
    Replace BD= 2. BM and BN= ½. BA we have
    P(B)= BF.BH= BM.BA => A, M, F, H are cocyclic

    ReplyDelete