CIRCLE AND THEIR THEORIES

🔵 Animated Circle Geometry – Class 9 & 10

📗 Rotating Radius (Angle Concept)

Animated radius shows how central angles change continuously.

📘 Angle at Centre = 2 × Angle at Circumference

Green animated lines highlight the angle at circumference.

📙 Tangent Perpendicular to Radius

The blinking tangent shows it is perpendicular to radius OA.

📐 Animated Circle Theorems with Examples (Class 9–10)

1️⃣ Angle at Centre = 2 × Angle at Circumference

Central angle is double the angle at the circumference.

Example:
If angle at circumference = 30°, then central angle = 2 × 30° = 60°.

2️⃣ Angles in the Same Segment are Equal

Angles subtended by the same chord are equal.

Example:
If ∠ACB = 45°, then ∠ADB = 45°.

3️⃣ Angle in a Semicircle = 90°

Angle made by a diameter is always 90°.

Example:
If AB is a diameter and C lies on the circle, then ∠ACB = 90°.

4️⃣ Cyclic Quadrilateral – Opposite Angles = 180°

Opposite angles of a cyclic quadrilateral add to 180°.

Example:
If ∠A = 70°, then opposite ∠C = 180° − 70° = 110°.