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

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

Details: Click on the figure below.

## Tuesday, February 21, 2017

### Geometry Problem 1317: Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence

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Draw C`B` tg to O at F` and // to DE. Join F to H and extend at A` (AE extended)

ReplyDeleteDraw A`A´` (A`` at AD extended) perpendicular to AO extended, join C` to midpoint of A`A``

Like P1315 => result

Join F to H need to be Join F` to H

ReplyDeleteTo c.t.e.o

ReplyDeleteSee below for the sketch per your solution as above.

https://goo.gl/photos/ugcUvNraGe6JuUgH7

Suppose that the result of Pr1315 is correct. I don't see how the result of Pr1315 help to prove that DG+HE= GH . please explain

Peter Tran

If you complete drawings, join C`, B` to M and C`, B` to midpoint of A`A``

ReplyDeleteTriangles formed by B`C` and points M and midpoint of A`A`` are isoceles so

segment parts on DE are equal

About point T of P1315

If T move counterclockwise, C move right up, and A move left down , so G move

towards M and N towards E so DG get bigger so and MN at the same length

So DG, MN are dependent from T