Geometry Problem. Post your solution in the comment box below.

Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

## Wednesday, July 11, 2018

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

Subscribe to:
Post Comments (Atom)

let P be midpoint of AB, then Point P lies on circle C1. D,F,H and P are concyclic.

ReplyDeleteHence 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.

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

ReplyDeleteDraw 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