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Arisa
1 day ago
6

The vertices of a triangle lie on the circumference of a circle. If its sides are 2.5 cm, 6 cm, and 6.5 cm, what is the area of

the circle (in
c
m
2
)?
Mathematics
1 answer:
Zina [9.1K]1 day ago
3 0

Response:

The area of the circle is roughly 33.183 cm²

Step-by-step explanation:

The lengths of the inscribed triangle are 2.5 cm, 6 cm, and 6.5 cm

Using the cosine law, we find;

6.5² = 6² + 2.5² - 2 × 6 × 2.5 × cos A

2 × 6 × 2.5 × cos A = 6² + 2.5² - 6.5² = 0

∴ cos(A) = 0

A = cos⁻¹(0) = 90°

The angle at the center is double the angle at the circumference

Thus, angle at the center = 2 × 90° = 180°

The 6.5 cm side forms a straight angle of 180° at the center of the circle; hence, this side equals the diameter of the circle

The circle's radius = 1/2 × The diameter = 1/2 × 6.5 cm = 3.25 cm

The area of the circle is determined by the formula π × r² = π × 3.25² ≈ 33.183 cm².

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25 one-dollar bills, 13 five-dollar bills, and 12 ten-dollar bills.

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