Coordinate Geometry · Mathematics

Radical Axis Simulation

Drag two (or three) circles and watch the radical axis S₁ − S₂ = 0 move with them. Tangent lengths from any point on the axis stay equal.

Interactive virtual lab · no download · works on phones and laptops

Chapter: Circles
For: Class 11 · JEE
Time: ~10 min

Radical Axis is a Pro simulation

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How to use it

1Drag a centre to move a circle; drag the ring handle to resize it.
2Drag the point P along the axis and compare the tangent lengths.
3Turn on the third circle to find the radical centre.

What to notice

The axis is always perpendicular to the line joining the centres.
When the circles intersect, the axis is their common chord.
From any point on the axis the two tangent lengths are equal.
Concentric circles have no radical axis.
Three circles with non-collinear centres share one radical centre.

For teachers

A ready-made teaching kit comes with this lab

Lesson plan
20 min, 4 steps
Ask the class
3 questions with answers
Quick quiz
7 questions, printable
Key formulas
2 formulas

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About the Radical Axis simulation

The radical axis of two circles is the set of points from which the tangents to both circles have equal length — the points with equal power with respect to both. It is always a straight line perpendicular to the line of centres, found by subtracting the two circle equations. For three circles the three radical axes meet at the radical centre.

In this radical axis simulation you drag two or three circles, move a point P and see its tangents to each circle, keep P on the axis to check the tangents stay equal, and find the radical centre. It covers Circles in Class 11 coordinate geometry and JEE.

Also covers: coaxial circles, radical centre, power of a point.