Tangent-Radius Perpendicularity Proof
Interactive geometric proof demonstrating why tangent lines are perpendicular to radii
0°
0.0
Live Data
Distance OP
(radius)
3.00
Distance OQ
(variable)
-
Angle at P
(tangent ⊥ radius)
90.0°
Ratio OQ/OP
(how much longer)
-
Updates in real-time
Learning Objectives
- • Understand the perpendicular relationship between tangents and radii
- • Apply the shortest distance principle in geometric proofs
- • Visualize abstract geometric concepts through interaction
Quick Tips
- 💡 Try dragging P to different positions on the circle
- 💡 Move Q far from P to see the distance difference clearly
- 💡 Notice how the angle marker always shows 90°