Problem Solving. Geometry and patterns.

Problem solving using mathematics

STEP 1: Identify the request.
What does the problem ask for?

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.

The problem solving process.

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 of Mathematical Problem Solving.

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