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Broad Topics >

Coordinates and Coordinate Geometry > Cartesian equations of circles

##### Age 14 to 18 Challenge Level:

Here is a pattern for you to experiment with using graph drawing
software. Find the equations of the graphs in the pattern.

##### Age 16 to 18 Challenge Level:

Show that there are infinitely many rational points on the unit
circle and no rational points on the circle x^2+y^2=3.

##### Age 16 to 18 Challenge Level:

Investigate the number of points with integer coordinates on
circles with centres at the origin for which the square of the
radius is a power of 5.

##### Age 16 to 18 Challenge Level:

Can you find the area of the central part of this shape? Can you do it in more than one way?

##### Age 16 to 18 Challenge Level:

Given any three non intersecting circles in the plane find another
circle or straight line which cuts all three circles orthogonally.

##### Age 16 to 18 Challenge Level:

A small circle fits between two touching circles so that all three
circles touch each other and have a common tangent? What is the
exact radius of the smallest circle?