Multiple choice

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?

  1. 60

  2. 80

  3. 120

  4. 160

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a right triangle with hypotenuse c and altitude h to the hypotenuse, the area is 1/2 * c * h. Also, area is 1/2 * x * y. The hypotenuse c is the diameter of the circumcircle, so c = 2 * 10 = 20. Area = 1/2 * 20 * 8 = 80. Thus, 1/2 * xy = 80, so xy = 160.

AI explanation

The triangle is inscribed in a circle of radius 10 cm, so the hypotenuse AC acts as the diameter making its length 20 cm. The area of a right triangle can be expressed as half the product of its legs (xy/2) or half the product of its hypotenuse and its altitude (20 * 8 / 2). Equating the two areas gives xy/2 = 80, so xy = 160. The result is 160.