# Triangle Construction

• Sep 30th 2008, 05:39 PM
GoldendoodleMom
Triangle 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 PM
Soroban
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 AM
msertic
Triangle 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.