Hello,

I have a math test after the holidays and I should be able to do this.

Our notes are quite confusing.

## Answer

Dear Stephen,

First of all, you should ask the teacher for additional explanations. The “I have a question” website can never replace a skilled subject teacher.

Below is a construction for the problem. It is best to view the different steps together in the attached figures. The solution below is only 1 possibility; maybe there are other and shorter methods…

Problem statement: given a segment and an angle, construct a right triangle of which the length of the radius of the inscribed circle is equal to the given segment and of which 1 of the angles is equal to the given angle.

Construction:

-Draw the circle with the given vertex as center and the given radius as radius.

-Extend one leg of the given angle and determine the opposite intersection with the circle. At that point of intersection, construct the tangent to the circle.

-Construct the perpendicular to the same leg of the given angle in the vertex. Determine the intersections with the circle and construct the tangent to the circle at one intersection.

-Construct the intersection of the other leg of the given angle with the circle and in that intersection construct the tangent to the circle.

-The intersections of the 3 tangents define a triangle that meets the requirements.

Note that no proof is given here that this construction is correct; after all, one still has to show that the triangle indeed meets all the conditions (for example, that it is a right triangle).

The attached drawings were made using the GeoGebra program.

Kind regards,

Peter Audenaert

## Answered by

#### Peter Audenaert

http://www.ugent.be

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