Baby Circle
Why do this problem?
This
question uses the formula for the distance between two points
and leads naturally to the formula for the equation of a circle. It
could be used to introduce the formula for the circle.
The problem also involves the use of geometrical properties of
circles, the use of Pythagoras Theorem and manipulation of
surds.
Possible approach
Either individually, in pairs or groups, or as a class, the
learners should plan how they are going to tackle this problem (see
Key Questions).
Key questions
What information is given?
What have we to find, the unknown(s)?
What information can we use from the geometrical properties of the
diagram?
How can we use the information to write down expressions
involving the unknown that can be put together to make up an
equation?
Extension:
(Thank you Bernard Murphy for these suggestions ) There are
lots of other opportunities for the learners to ask their own
questions here: e.g. In a square of side 2, draw four circles
diameter 1 touching a central circle of radius $r$. What is $r$?
Ask students to submit their questions along these lines rather
than just find answers to given questions. You could include a
graphic calculator activity, asking for equations of circles in
given diagrams such as Olympic Rings, circles within circles,
circles centred on $y=2x$ touching each other and axes
etc.