The radius of circum-circle of a right-angled triangle is 10 cm and the altitude drawn to the hypotenuse is 8 cm. What is the area of the triangle?
- A. 60\text{ cm}^{2}
- B. 80\text{ cm}^{2} ✓
- C. 100\text{ cm}^{2}
- D. 120\text{ cm}^{2}
Correct Answer: B. 80\text{ cm}^{2}
Explanation
In a right-angled triangle, the circumcenter is the midpoint of the hypotenuse. Thus, the hypotenuse is the diameter of the circumcircle: 2 \times 10 = 20\text{ cm}. Area = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 8 = 80\text{ cm}^2.
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