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.
