Question

Points $A$, $B$, and $C$ are on a circle such that $AB = 8$, $BC = 15$, and $AC = 17$. Find the radius of the circle.

Answer 1

Answer:radius is 8.5

Explanation:

Points A, B, and C are on a circle such that AB = 8, BC = 15, and AC = 17. Looking at the three points, they form a Pythagorean triple. This is so because

17^2 = 8^2 + 15^2

289 = 64 + 225 = 289

This means that the triangle formed by the three points is a right angle triangle. A right angle triangle inscribed in a circle subtends an angle of 90 on the circumference of the circle. This means that the longest side or hypotenuse of the triangle becomes the diameter of the circle. Therefore,

Diameter = 17

Radius = diameter /2 = 17/2 = 8.5

Answer 2

8.5 units

Explanation:

Using Pythagoras theorem, it will be observed that 8, 15 and 17 are Pythagorean triple

AB² + BC² = AC²

8² + 15² = 64 + 225 = 289 = 17²

therefore ABC is a right angle triangle with right angle at vertex B and AC is it hypotenuse. Since B is on the circumference and is 90°, then it must subtend a diameter.

AC = diameter of the circle

radius = diameter / 2 = 17 / 2 = 8.5 units