Does anyone have an algorithm for constructing a triangle given one side, AB, and altitudes h and k from A and B respectively? (Using straightedge compass construction)

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- Sep 30th 2008, 05:39 PMGoldendoodleMomTriangle Construction
Does anyone have an algorithm for constructing a triangle given one side, AB, and altitudes h and k from A and B respectively? (Using straightedge compass construction)

- Sep 30th 2008, 06:20 PMSoroban
Hello, GoldendoodleMom!

Quote:

Find an algorithm for constructing a triangle given one side, $\displaystyle AB$,

and altitudes $\displaystyle h$ and $\displaystyle k$ from $\displaystyle A$ and $\displaystyle B$ respectively.

(Using straightedge-compass construction)

Draw line segment $\displaystyle AB.$

Locate its midpoint $\displaystyle M.$

Draw a semicircle with diameter $\displaystyle AB.$Code:`* * *`

* *

* *

* *

* *

A * - - - - * - - - - * B

M

With $\displaystyle A$ as center and radius $\displaystyle h$, swing an arc cutting the semicircle at $\displaystyle P.$

With $\displaystyle B$ as center and radius $\displaystyle k$, swing an arc cutting the semicircle at $\displaystyle Q.$

Code:`Q`

∆ * * P

* ∆ o

* ∆ *

* o ∆ *

o ∆

* o ∆ *

A o - - - - * - - - - ∆ B

M

Draw $\displaystyle AQ$ and $\displaystyle BP$, extending them to meet at $\displaystyle C.$

The required triangle is $\displaystyle \Delta ABC.$

- Feb 13th 2009, 05:52 AMmserticTriangle Construction
Hello (Happy)

For the past few days, I've been searching on the Internet for a triangle construction from its orthocenter, circumcenter and incenter. Unfortunately,I didn't find anything. Does anyone know something about this construction?

Thank you.