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### Construct Triangle ABC Given Altitude...

```Date: 04/11/2002 at 16:37:33
From: Michael Wright
Subject: Constructing a triangle ABC

The problem I am working on is as follows:

Given the altitude from vertex A, angle BAC, and the radius of the
circumscribed circle, construct triangle ABC.

I am trying to solve this problem using the Geometer's Sketchpad, but
keep running into dead ends. If you can figure this out, it would be
greatly appreciated.

Thank you,
Michael Wright
```

```
Date: 04/11/2002 at 17:34:13
From: Doctor Floor
Subject: Re: Constructing a triangle ABC

Hi, Michael,

We can do the construction as follows. Start by drawing a circle S

From a point X on the circle inscribe an angle of the given magnitude
of angle BAC in the circle. The legs of this angle intersect the
circle for a second time in two points, which we take to be the
endpoints of BC. Now BC must be of the good length, since it is
intercepted by an inscribed angle of the good magnitude. Of course
vertex A must be on this circle as well, at the same side of BC as X.

From B draw a line L perpendicular to BC, and draw a circle C' with
center B and the given altitude length as radius. C' and L intersect
in two points, of which we take the one at the same side of BC as X to
be D. Now through D draw a line M parallel to BC. All points of M are
at the right distance from BC to be a possible vertex A.

Now the intersections of S and M are possible locations for A. And we
are done.

If you have more questions, just write back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Constructions

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