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A circle is inscribed in a square. An equilateral triangle of side 4√3 cm is inscribed in that circle. The length of the diagonal of the square (in centimetres) is
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- 4√2
- 8
- 8√2
- 16
- 4√2
Correct Option: C
Area of equilateral triangle ABC
| = | × (4√3)² | = 12√3 cm² | ||
| 4 | 4 |
Again, AD is the height and O is the centre of the circle
∴ Area of ∆ ABC
| = | × BC × AD | |
| 2 |
| ⇒ 12√3 = | × 4√3 × AD | |
| 2 |
| ⇒ AD = | = 6 | |
| 2√3 |
| ∴ OD = | AD = 2 cm | |
| 3 |
∴ OB = √BD² + OD²
= (2√3)² + 2²
= √16 = 4 cm.
∴ Side of square = 2 × OB = 2 × 4 = 8 cm.
∴ Diagonal of square = √2 × Side = 8√2 cm
