Answer:
The area of the circle is approximately 33.183 cm²
Step-by-step explanation:
The sides of the inscribed triangle are 2.5 cm, 6 cm, and 6.5 cm
By cosine rule, we have;
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 subtended at the center = 2 × Angle subtended at the circumference
Therefore, angle at the center = 2 × 90° = 180°
The 6.5 cm side forms an angle of 180° (a straight line) at the center of the circle and therefore, the 6.5 cm side = The diameter of the circle
The radius of the circle = 1/2 × The diameter of the circle = 1/2 × 6.5 cm = 3.25 cm
The area of the circle = π × r² = π × 3.25² ≈ 33.183 cm².
