Find the radius of a circle circumscribed about an isosceles right-angled triangle if the perpendicular

Find the radius of a circle circumscribed about an isosceles right-angled triangle if the perpendicular to the hypotenuse is: 1) 12 cm 2) 1.5 dm 3) 32 mm

Since the triangle ABC is rectangular and isosceles, its height drawn to the hypotenuse of the AC is also the bisector and median.

The median of a right-angled triangle drawn to the hypotenuse is equal to half the length of the hypotenuse. BH = AH = CH = AC / 2.

Since the angle ABC = 90, the arc AC = 180, which means the hypotenuse AC is the diameter of the circle.

Then, with BH = 12 cm, R = 12 cm, with BH = 1.5 dm, R = 1.5 dm, with BH = 32 mm, R = 32 mm.

Answer: BH = R.