2024 · Q84
The area of the circle circumscribing three identical circles touching each other is π(2 + √3)²/3 square cm. What is the radius of one of the smaller circles?
Elementary MathematicsCircles
- A0.5 cm
- B1 cm
- C1.5 cm
- D3 cm
Explanation
The three base centres form an equilateral triangle of side 3+3 = 6 cm. Its circumradius is 6/√3 = 2√3 cm. Each cone's vertex sits directly above its base centre, so the circle through the three vertices is congruent to the base-centre circumcircle. Its area is π(2√3)² = 12π sq cm — option D.