What is the area of a right-angled triangle, if the radius of the circumcircle is 5 cm and altitude drawn to the hypotenuse is 4 cm?
- A. 20 \text{ cm}^{2} ✓
- B. 18 \text{ cm}^{2}
- C. 16 \text{ cm}^{2}
- D. 10 \text{ cm}^{2}
Correct Answer: A. 20 \text{ cm}^{2}
Explanation
In a right-angled triangle, the circumcenter is the midpoint of the hypotenuse. Thus, the hypotenuse acts as the diameter of the circumcircle, meaning hypotenuse = 2 \times 5 = 10 \text{ cm}. Area = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times \text{hypotenuse} \times \text{altitude} = \frac{1}{2} \times 10 \times 4 = 20 \text{ cm}^2.
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