**
STEP 2: Respond to the request.
Ask "
How Would I Find Out ?
"
**

**
STEP 3: Generate the result.
Ask "
What does the result tell me?
"
**

Problem Source: http://www.lincoln.ac.nz/educ/tip/39.htm

Solution presentation copyright Howard C. McAllister, 1998.

Given two intersecting straight lines and a point P marked on one of them, show how to construct a circle that is tangent to both lines including point P.

SOLUTION:

The problem asks for the location of the center of a circle that fulfills the stated conditions. The center of the circle will lie on a perpendicular drawn through P.

We are now asked to located a particular point on the perpendicular.

1) Draw a circle of radius X-P with center at X.

2) Construct a perpendicular at P'. The intersection of this with the previously drawn perpendicular defines the center of the circle sought.

3) Draw the circle of radius P-C with center at C.

Start a problem by responding to what is asked for. In the present case we are asked to draw a particular circle. To draw a circle the first thing one needs to know is the location of the center.The concept involved is that a tangent to a circle is perpendicular to a diameter of the circle.

The example is one of those presented by A. Schoenfeld to illustrate his well developed theory ofMathematical Problem Solving.

Comments are important and appreciated. Please comment.

A SureMath solution. Copyright 1998, Howard C. McAllister.