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There are **6** NRICH Mathematical resources connected to **Cartesian equations of circles**, you may find related items under Coordinates, functions and graphs.

Problem
Primary curriculum
Secondary curriculum
### Curved Square

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

Problem
Primary curriculum
Secondary curriculum
### Orthogonal Circle

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

Problem
Primary curriculum
Secondary curriculum
### Baby Circle

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rational Round

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

Problem
Primary curriculum
Secondary curriculum
### Square Pair Circles

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

Problem
Primary curriculum
Secondary curriculum
### Ellipses

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

Age 14 to 18

Challenge Level