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Two circles with centres A and B and radius 2 units touch each other externally at ‘C’. A third circle with centre ‘C’ and radius ‘2’ units meets other two at D and E. Then the area of the quadrilateral ABDE is
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- 2√2 sq. units
- 3√3 sq. units
- 3√2 sq. units
- 2√3 sq. units
- 2√2 sq. units
Correct Option: B
ABDE will be a trapezium
AB = 4 units
| DE = | AB = 2 units | |
| 2 |
FB = 1 unit, BD = 2 units.
⇒ DF = √2² - 1² = √3units
| ∴ Area of ABDE = | (AB + DE) × DF | |
| 2 |
| = | (4 + 2) × √3 | |
| 2 |
= 3√3 sq. units
