🔵 Radius of the Big Circle? | Geometry Problem with a Hidden Trick

🔵 Can you find the radius of the big circle using pure geometry — no guessing, no formulas, just logic?

In this video, we solve a beautiful circle geometry problem using classical theorems and triangle similarity.

✏️ Solution Strategy:

1️⃣ First, draw the radius of the small circle to the tangent point.
2️⃣ Use the geometry theorem:

📐 The radius drawn to a point of tangency is perpendicular to the tangent.

This creates a right angle and allows us to form two triangles.

3️⃣ Then apply similar triangles:

🔁 Corresponding sides of similar triangles are proportional.

We write the ratio of corresponding sides, use the given length 12, and substitute it into the ratio equation.

4️⃣ This gives the radius of the small circle.

5️⃣ Since the radii are in the ratio 1 : 3, we simply triple the small radius to get the radius of the big circle.

🎯 This problem beautifully combines:

Tangent–radius theorem

Triangle similarity

Proportional reasoning

Circle geometry fundamentals

Perfect for:

High school geometry

Olympiad-style problems

Exam preparation

Conceptual learning

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