Worked Examples - Concentric Circles

Current Scene: Welcome

Outer Radius: 150px

Inner Radius: 90px

Current Example: None

Relationship: Concentric

📊 Mathematical Solution

Select an example to see the mathematical solution

🎯 Chord Tangent to Inner Circle

When a chord of the larger circle touches the smaller circle, it is bisected at the point of contact. This demonstrates the perpendicular from center theorem.

AP = BP (Chord is bisected)

🔄 Area Between Circles (Annulus)

The area of the ring region between concentric circles equals π times the difference of the squares of their radii.

Area = π(R² - r²)

📐 Common Tangents

Concentric circles have no external common tangents because they share the same center. Any tangent to one circle intersects the other.

No external tangents

⚡ Power of a Point

For any external point and secant through concentric circles, the difference in powers relates to the area of the annulus.

Power difference = π(R² - r²)