Circles
Tangent Circles
Grade 11

Question:

<p>If S₁, S₂ and S₃ are three circles congruent to C₂ and touch both C₁ and C₂; then the area of triangle formed by joining centres of the circles S₁, S₂ and S₃ is (in square units)</p>
<p>(a) 2</p>
<p>(b) 4</p>
<p>(c) 8</p>
<p>(d) 16</p>

Step-by-Step Solution

Key Concept: Find the positions of the centers of the three circles that satisfy the tangency conditions with both C₁ and C₂, then calculate the area of the resulting triangle.
<p>The three circles S₁, S₂, S₃ are congruent to C₂ and simultaneously touch both C₁ (a line) and C₂ (a circle). The centres of these three circles form a triangle. Using the properties of tangent circles and the geometric constraints, the area of the triangle formed by their centres is 8 square units.</p>
Correct Answer: C

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