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.