A right-angled triangle ABC is inscribed in a circle of radius 10 cm. The altitude drawn to the hypotenuse AC is of length 8 cm. If AB=x cm and BC=y cm, then what is the value of xy?

Explanation

In a right-angled triangle inscribed in a circle, the hypotenuse is the diameter, so AC = 2 \times 10 = 20\text{ cm}. The area of \triangle ABC is \frac{1}{2} \times AC \times \text{altitude} = \frac{1}{2}(20)(8) = 80. Also, the area is \frac{1}{2}xy. Thus, \frac{1}{2}xy = 80 \implies xy = 160.

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