Step {{ step }} of 5

Tangent & Radius

A tangent line is perpendicular to the radius at the point of tangency.

touch_app Drag point T around the circle

Angle is always 90°

Intersecting Chords

When two chords intersect, the products of their segments are equal:

tune Slide to balance
{{ s2_data.a }} × {{ s2_data.b }} {{ s2_data.a * s2_data.b }}
=
{{ s2_data.c }} × {{ s2_val }} {{ s2_data.c * s2_val }}

Tangent & Secant

The square of the tangent equals the outer secant times the whole secant:

pan_tool Drag to build formula
t
² =
o
· (
o
+ x )
{{ chip.val }}

Two Secants

Outer × Whole = Outer × Whole

add_circle Adjust to solve
Find the missing inner segment x
{{ s4_data.o1 }} × {{ s4_data.o1 + s4_data.i1 }} = {{ s4_data.o1 * (s4_data.o1 + s4_data.i1) }}
=
{{ s4_data.o2 }} × ({{ s4_data.o2 }} +
{{ s4_val }}
)
Current Product: {{ s4_data.o2 * (s4_data.o2 + s4_val) }}

Mastered!

You've successfully explored the relationships between chords, secants, and tangents.